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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_5f8d949c-9812-467a-8439-24df14f0d54f_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Assets and Liabilities of Consolidated VIEs</link:label>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_019bf84d-4f6a-7f6e-bf26-87483b1f5f9a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Holdback for representations and warranties</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Incurred</link:label>
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    <link:label id="lab_srt_MortgageLoansOnRealEstatePrincipalAmountOfDelinquentLoans_f6157959-a58e-4fd3-8b29-4d79e035f6b6_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstatePrincipalAmountOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid principal balance</link:label>
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    <link:label id="lab_srt_MortgageLoansOnRealEstatePrincipalAmountOfDelinquentLoans_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstatePrincipalAmountOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Principal Amount of Delinquent Loans</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract_2f957bb9-4ebf-435d-aacc-176547a519d0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OTHER COMPREHENSIVE INCOME</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossTaxAbstract"/>
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    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
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    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
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    <link:label id="lab_adam_BusinessPurposeLoansMember_b2e1c234-e547-4d96-94a1-215985fba501_terseLabel_en-US" xlink:label="lab_adam_BusinessPurposeLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business purpose loans</link:label>
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    <link:label id="lab_adam_BusinessPurposeLoansMember_documentation_en-US" xlink:label="lab_adam_BusinessPurposeLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Purpose Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BusinessPurposeLoansMember" xlink:href="adam-20251231.xsd#adam_BusinessPurposeLoansMember"/>
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    <link:label id="lab_adam_InterestRateStepUpAxis_0b13712a-97ef-4acb-839c-a9b508e2228e_terseLabel_en-US" xlink:label="lab_adam_InterestRateStepUpAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Axis]</link:label>
    <link:label id="lab_adam_InterestRateStepUpAxis_label_en-US" xlink:label="lab_adam_InterestRateStepUpAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Axis]</link:label>
    <link:label id="lab_adam_InterestRateStepUpAxis_documentation_en-US" xlink:label="lab_adam_InterestRateStepUpAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_InterestRateStepUpAxis" xlink:href="adam-20251231.xsd#adam_InterestRateStepUpAxis"/>
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    <link:label id="lab_adam_GainOnRepurchaseOfPreferredStock_25ad751b-dd72-4f6d-bf49-80bd73c83d7b_terseLabel_en-US" xlink:label="lab_adam_GainOnRepurchaseOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on repurchase of preferred stock</link:label>
    <link:label id="lab_adam_GainOnRepurchaseOfPreferredStock_82387fb3-ff1d-402d-a289-fcdbf666e449_verboseLabel_en-US" xlink:label="lab_adam_GainOnRepurchaseOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Plus: Gain on repurchase of Preferred Stock</link:label>
    <link:label id="lab_adam_GainOnRepurchaseOfPreferredStock_label_en-US" xlink:label="lab_adam_GainOnRepurchaseOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain on Repurchase of Preferred Stock</link:label>
    <link:label id="lab_adam_GainOnRepurchaseOfPreferredStock_documentation_en-US" xlink:label="lab_adam_GainOnRepurchaseOfPreferredStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain on Repurchase of Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_GainOnRepurchaseOfPreferredStock" xlink:href="adam-20251231.xsd#adam_GainOnRepurchaseOfPreferredStock"/>
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    <link:label id="lab_us-gaap_PaymentsToPurchaseMortgageLoansHeldForSale_019c22e9-374c-78d1-af26-a108feab6d5f_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToPurchaseMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal balance of loans acquired through business combination</link:label>
    <link:label id="lab_us-gaap_PaymentsToPurchaseMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_PaymentsToPurchaseMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Purchase, Loan, Mortgage, Held-for-Sale</link:label>
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    <link:label id="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment_019be4fe-3f8a-71f8-a8c7-44c064972a67_terseLabel_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MSRs received from equity investment in Constructive</link:label>
    <link:label id="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment_label_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights Received From Equity Investment</link:label>
    <link:label id="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment_documentation_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromEquityInvestment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights Received From Equity Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageServicingRightsReceivedFromEquityInvestment" xlink:href="adam-20251231.xsd#adam_MortgageServicingRightsReceivedFromEquityInvestment"/>
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    <link:label id="lab_adam_ScheduleOfComponentsOfIncomeFromRealEstateAndExpensesTableTextBlock_352971a8-8bd4-494f-890e-f6e04b7066a1_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfComponentsOfIncomeFromRealEstateAndExpensesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Income from Real Estate and Expenses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfComponentsOfIncomeFromRealEstateAndExpensesTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfComponentsOfIncomeFromRealEstateAndExpensesTableTextBlock"/>
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    <link:label id="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock_14004044-b53a-44f1-8efb-5b9deaf599fa_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on preferred stock</link:label>
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    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfBuildingsAndImprovements_084aafcb-10cd-45eb-8bea-8509746a9ea9_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfBuildingsAndImprovements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings and Improvements</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfBuildingsAndImprovements_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfBuildingsAndImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Building and Improvements, Amount</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_8de6e8d9-5fe3-46e5-89ca-f02cd4a44108_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
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    <link:label id="lab_adam_InvestmentinUnconsolidatedEntitiesMember_167f6f01-fa4f-4a06-b140-ab2b822213fd_terseLabel_en-US" xlink:label="lab_adam_InvestmentinUnconsolidatedEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity investments, at fair value</link:label>
    <link:label id="lab_adam_InvestmentinUnconsolidatedEntitiesMember_label_en-US" xlink:label="lab_adam_InvestmentinUnconsolidatedEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment in Unconsolidated Entities [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_InvestmentinUnconsolidatedEntitiesMember" xlink:href="adam-20251231.xsd#adam_InvestmentinUnconsolidatedEntitiesMember"/>
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    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_2bed9eae-71f6-4286-83fa-394fcf58d6c8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total (Loss) Income - Multi-Family Preferred Equity Ownership Interests</link:label>
    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_3bf5ab3e-23c2-4bc5-b0f4-cf0088bd36eb_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value, gain (loss)</link:label>
    <link:label id="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1_label_en-US" xlink:label="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Option, Changes in Fair Value, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOptionChangesInFairValueGainLoss1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:to="lab_us-gaap_FairValueOptionChangesInFairValueGainLoss1" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNumberOfLoans_f0794870-b2d8-4882-a7b7-994ae9757cdb_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Loans</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateNumberOfLoans_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateNumberOfLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Number of Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateNumberOfLoans" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateNumberOfLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateNumberOfLoans" xlink:to="lab_srt_MortgageLoansOnRealEstateNumberOfLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestRateCapMember_71505eee-b158-4445-b330-e3e809f26780_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate caps</link:label>
    <link:label id="lab_us-gaap_InterestRateCapMember_label_en-US" xlink:label="lab_us-gaap_InterestRateCapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Cap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestRateCapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestRateCapMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestRateCapMember" xlink:to="lab_us-gaap_InterestRateCapMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_3c251705-a425-4072-b119-967c74e7074e_totalLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current income tax provision</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_ee1d8ade-ab99-4b83-a464-aad6adade720_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_57a16cc0-6891-4f51-b689-08bc6644240b_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic concentrations</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract_717e3a20-7852-4bd5-b614-61b054fa3c3a_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Initial Cost to Company</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Initial Cost [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract" xlink:to="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ConsolidatedSLSTMember_f94ff073-3212-4524-b05c-887c8788b6b6_terseLabel_en-US" xlink:label="lab_adam_ConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated SLST</link:label>
    <link:label id="lab_adam_ConsolidatedSLSTMember_6554a19f-df32-4d72-bde1-7503a35b81ff_verboseLabel_en-US" xlink:label="lab_adam_ConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Consolidated SLST at fair value</link:label>
    <link:label id="lab_adam_ConsolidatedSLSTMember_label_en-US" xlink:label="lab_adam_ConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated SLST [Member]</link:label>
    <link:label id="lab_adam_ConsolidatedSLSTMember_documentation_en-US" xlink:label="lab_adam_ConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consolidated SLST [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ConsolidatedSLSTMember" xlink:href="adam-20251231.xsd#adam_ConsolidatedSLSTMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ConsolidatedSLSTMember" xlink:to="lab_adam_ConsolidatedSLSTMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_1b2aea1a-ff83-4fe9-9972-4b698f41e198_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock based compensation expense, net</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_OH_019b922c-d871-7edc-ae56-dd4304566343_terseLabel_en-US" xlink:label="lab_stpr_OH" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ohio</link:label>
    <link:label id="lab_stpr_OH_label_en-US" xlink:label="lab_stpr_OH" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OHIO</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_OH" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_OH"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_OH" xlink:to="lab_stpr_OH" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialInstrumentInterestTypeDomain_019b0754-a148-726c-b877-fa0362ababb3_terseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentInterestTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument Interest Type [Domain]</link:label>
    <link:label id="lab_adam_FinancialInstrumentInterestTypeDomain_label_en-US" xlink:label="lab_adam_FinancialInstrumentInterestTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument Interest Type [Domain]</link:label>
    <link:label id="lab_adam_FinancialInstrumentInterestTypeDomain_documentation_en-US" xlink:label="lab_adam_FinancialInstrumentInterestTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Instrument Interest Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialInstrumentInterestTypeDomain" xlink:href="adam-20251231.xsd#adam_FinancialInstrumentInterestTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialInstrumentInterestTypeDomain" xlink:to="lab_adam_FinancialInstrumentInterestTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateOtherAdditions_97db80d7-abbc-400a-8905-cac77517512b_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers in</link:label>
    <link:label id="lab_us-gaap_RealEstateOtherAdditions_label_en-US" xlink:label="lab_us-gaap_RealEstateOtherAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Other Addition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOtherAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateOtherAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOtherAdditions" xlink:to="lab_us-gaap_RealEstateOtherAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_68e0347e-42a6-45e5-9fd7-308e4d52e54c_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock_ae9c0295-f16e-4371-9795-3498b2131cf9_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Interest Income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income and Interest Expense Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock" xlink:to="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GranteeStatusDomain_47b5d0bc-749f-4d83-99cc-4fd11743dbc5_terseLabel_en-US" xlink:label="lab_us-gaap_GranteeStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grantee Status [Domain]</link:label>
    <link:label id="lab_us-gaap_GranteeStatusDomain_label_en-US" xlink:label="lab_us-gaap_GranteeStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Grantee Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GranteeStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GranteeStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GranteeStatusDomain" xlink:to="lab_us-gaap_GranteeStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CorpusChristiTXMember_2fef824f-3f55-4221-aac8-66a5244b2ab4_terseLabel_en-US" xlink:label="lab_adam_CorpusChristiTXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corpus Christi, TX</link:label>
    <link:label id="lab_adam_CorpusChristiTXMember_label_en-US" xlink:label="lab_adam_CorpusChristiTXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corpus Christi, TX [Member]</link:label>
    <link:label id="lab_adam_CorpusChristiTXMember_documentation_en-US" xlink:label="lab_adam_CorpusChristiTXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Corpus Christi, TX</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CorpusChristiTXMember" xlink:href="adam-20251231.xsd#adam_CorpusChristiTXMember"/>
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    <link:label id="lab_adam_MortgageLoansonRealEstateDeductionsAbstract_1d098623-bb2e-445e-b5db-a85c2efa70b6_terseLabel_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateDeductionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deductions during period:</link:label>
    <link:label id="lab_adam_MortgageLoansonRealEstateDeductionsAbstract_label_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateDeductionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Deductions [Abstract]</link:label>
    <link:label id="lab_adam_MortgageLoansonRealEstateDeductionsAbstract_documentation_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateDeductionsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Deductions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageLoansonRealEstateDeductionsAbstract" xlink:href="adam-20251231.xsd#adam_MortgageLoansonRealEstateDeductionsAbstract"/>
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    <link:label id="lab_us-gaap_DividendsCommonStockCash_0478f485-34d4-45b2-9062-8f7d361aadd5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared on common stock</link:label>
    <link:label id="lab_us-gaap_DividendsCommonStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsCommonStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Common Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsCommonStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsCommonStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsCommonStockCash" xlink:to="lab_us-gaap_DividendsCommonStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_7f9c9b25-587e-45e8-99da-db31c66e686e_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Company's stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_77fbdd5b-3e73-4213-b658-e434e357969b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_722af55e-2bee-453f-92bd-6e71586add38_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
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    <link:label id="lab_stpr_NY_c6df7d21-f848-47e5-9b6f-cc386c9810de_terseLabel_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New York</link:label>
    <link:label id="lab_stpr_NY_label_en-US" xlink:label="lab_stpr_NY" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NEW YORK</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_NY" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_NY"/>
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    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_26c5713e-e40f-4da9-a02f-65bf6ee54591_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_2088920e-b764-45cb-bd86-79a79fdc862c_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock issued (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_64a0f46f-eb1e-4b0c-b41c-249a8289539d_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Assets:</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments, Financial Assets, Balance Sheet Groupings [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:to="lab_us-gaap_FinancialInstrumentsFinancialAssetsBalanceSheetGroupingsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_f3a23997-8e6e-4b57-b981-6937210714be_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_e0bc3f7d-0fb8-4324-84f0-b151211d2a74_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Recurring</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsRecurringMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsRecurringMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsRecurringMember" xlink:to="lab_us-gaap_FairValueMeasurementsRecurringMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDerivatives_019c2ea4-17eb-7b54-8417-e2776139f2ec_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesDerivatives_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_61e9273d-9f0b-40f3-92ee-a27ea48e826c_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES AND EQUITY</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances_3f4bb706-5661-4b67-ab61-12b5e7633214_terseLabel_en-US" xlink:label="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recoverable advances on residential loans</link:label>
    <link:label id="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances_label_en-US" xlink:label="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, After Allowance For Credit Loss, Recoverable Advances</link:label>
    <link:label id="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances_documentation_en-US" xlink:label="lab_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, After Allowance For Credit Loss, Recoverable Advances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances" xlink:href="adam-20251231.xsd#adam_FinancingReceivableAfterAllowanceForCreditLossRecoverableAdvances"/>
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    <link:label id="lab_dei_CoverAbstract_86eeb111-8b9b-48ff-8752-e98e69b44843_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_b93d23b4-d322-4be8-9ed9-555425689fa2_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, estimated fair value</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:to="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_32c571f9-52e7-4839-8bc8-19f8ed2f0c21_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets and Liabilities of Disposal Group Held for Sale</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_b58dce5b-93c6-4a78-ad0e-1659e295fc01_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_TransferToOtherRealEstate_8ba1a7e3-bbfc-4265-85ca-b5235eb1b426_terseLabel_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer from residential loans to real estate owned</link:label>
    <link:label id="lab_us-gaap_TransferToOtherRealEstate_label_en-US" xlink:label="lab_us-gaap_TransferToOtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferToOtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferToOtherRealEstate"/>
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    <link:label id="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue_7e15d590-5886-4205-888f-8e97eacf3445_terseLabel_en-US" xlink:label="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reserved for future issuance</link:label>
    <link:label id="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue_label_en-US" xlink:label="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value Of Shares Reserved For Future Issuance, Value</link:label>
    <link:label id="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue_documentation_en-US" xlink:label="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Aggregate value of common shares reserved for future issuance.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:href="adam-20251231.xsd#adam_CommonStockValueOfSharesReservedForFutureIssuanceValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:to="lab_adam_CommonStockValueOfSharesReservedForFutureIssuanceValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_0b237561-f017-4fe6-8ac2-291d164cf39f_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-lived intangible asset, useful life</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_019bf84d-4f6a-7088-ad8f-d6d71cc8ccfe_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortization Period (Years)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife"/>
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    <link:label id="lab_us-gaap_SubordinatedBorrowingAxis_0370f13d-ef9c-4c1f-ac51-9434842cd692_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedBorrowingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated Borrowing [Axis]</link:label>
    <link:label id="lab_us-gaap_SubordinatedBorrowingAxis_label_en-US" xlink:label="lab_us-gaap_SubordinatedBorrowingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Borrowing [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedBorrowingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedBorrowingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedBorrowingAxis" xlink:to="lab_us-gaap_SubordinatedBorrowingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_66c5948a-f94a-409d-b3f4-5c7d85d3a99c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_754b8b5e-14bd-43ae-875c-18217b5b7dfd_negatedLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_52b9870b-8fc7-4833-9e8c-c021a337ccde_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to redeemable non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_ed7eef6f-4588-4d35-8ab6-2c85e1baeca1_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total net gains attributable to non-controlling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MeasurementInputCollateralPrepaymentRateMember_c5e3d169-5634-4d1f-a2db-3d2162b70072_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputCollateralPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral prepayment rate</link:label>
    <link:label id="lab_adam_MeasurementInputCollateralPrepaymentRateMember_label_en-US" xlink:label="lab_adam_MeasurementInputCollateralPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Collateral Prepayment Rate [Member]</link:label>
    <link:label id="lab_adam_MeasurementInputCollateralPrepaymentRateMember_documentation_en-US" xlink:label="lab_adam_MeasurementInputCollateralPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input Collateral Prepayment Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputCollateralPrepaymentRateMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputCollateralPrepaymentRateMember"/>
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    <link:label id="lab_adam_GWRGatewayPartnersLLCMember_b6239cbb-7aa5-4681-82be-88a0196a24f4_terseLabel_en-US" xlink:label="lab_adam_GWRGatewayPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GWR Gateway Partners, LLC</link:label>
    <link:label id="lab_adam_GWRGatewayPartnersLLCMember_label_en-US" xlink:label="lab_adam_GWRGatewayPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GWR Gateway Partners, LLC [Member]</link:label>
    <link:label id="lab_adam_GWRGatewayPartnersLLCMember_documentation_en-US" xlink:label="lab_adam_GWRGatewayPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GWR Gateway Partners, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_GWRGatewayPartnersLLCMember" xlink:href="adam-20251231.xsd#adam_GWRGatewayPartnersLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_GWRGatewayPartnersLLCMember" xlink:to="lab_adam_GWRGatewayPartnersLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_67344a09-b37b-441e-bb42-6992d79b2cfb_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_e7c99749-5a27-4889-85e2-0af337b019e7_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Lease intangibles, net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_PA_d22b670c-a63e-4913-9598-1ed2c85f204f_terseLabel_en-US" xlink:label="lab_stpr_PA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pennsylvania</link:label>
    <link:label id="lab_stpr_PA_019bf80c-a8c3-757a-bb5e-b4bad713336e_verboseLabel_en-US" xlink:label="lab_stpr_PA" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Pennsylvania</link:label>
    <link:label id="lab_stpr_PA_label_en-US" xlink:label="lab_stpr_PA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PENNSYLVANIA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_PA" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_PA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_PA" xlink:to="lab_stpr_PA" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold_019c420d-836d-71d9-9b28-dd45adca00d2_terseLabel_en-US" xlink:label="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt covenant, net cash to equity multiple threshold</link:label>
    <link:label id="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold_label_en-US" xlink:label="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Covenant, Net Cash To Equity Multiple Threshold</link:label>
    <link:label id="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold_documentation_en-US" xlink:label="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Covenant, Net Cash To Equity Multiple Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:href="adam-20251231.xsd#adam_DebtCovenantNetCashToEquityMultipleThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:to="lab_adam_DebtCovenantNetCashToEquityMultipleThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_98b95fad-1697-4930-9d8d-71825f0548e3_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationByPropertyTable_252a2bdf-6820-4afc-9188-61bf4259960f_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationByPropertyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, by Property [Table]</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationByPropertyTable_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationByPropertyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, by Property [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationByPropertyTable" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationByPropertyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationByPropertyTable" xlink:to="lab_srt_RealEstateAndAccumulatedDepreciationByPropertyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_f3ba11f2-1fe1-46c5-bfef-2f49637122fe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses)</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liability, Recurring Basis, Still Held, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_c846f25a-a326-4c6b-b97d-6802e0cde5b5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_88a719b1-bc3c-4e9e-b9a1-26c35201ab6f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts_bcbe6ba4-7c30-4ea1-b01b-c4db8f0b0327_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Adjustment to Basis</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Cost Capitalized Subsequent to Acquisition, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationCostsCapitalizedSubsequentToAcquisitionCarryingCosts"/>
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    <link:label id="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember_2413f6f4-62aa-4cc2-a27a-42d1ce5d9823_terseLabel_en-US" xlink:label="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Joint Venture Equity Investments in Multi-Family Properties</link:label>
    <link:label id="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember_019b0793-9796-7cba-b7a5-1c6cfb5ad675_verboseLabel_en-US" xlink:label="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Joint venture equity investments in multi-family properties</link:label>
    <link:label id="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember_label_en-US" xlink:label="lab_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture Equity Investments In Multi-family Properties [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember" xlink:href="adam-20251231.xsd#adam_JointVentureEquityInvestmentsInMultiFamilyPropertiesMember"/>
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    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember_5543283d-c687-4fb8-9da1-622a90633869_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period One</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodOneMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodOneMember"/>
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    <link:label id="lab_us-gaap_OtherAssetsMember_89e00e44-a079-4a41-8904-240ee04d009b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsMember"/>
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    <link:label id="lab_adam_ContractualMaturities_bcf9b461-dc22-4780-ba98-679f534f7a63_terseLabel_en-US" xlink:label="lab_adam_ContractualMaturities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contractual maturities (up to)</link:label>
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    <link:label id="lab_adam_ContractualMaturities_documentation_en-US" xlink:label="lab_adam_ContractualMaturities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contractual maturities of investments.</link:label>
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    <link:label id="lab_adam_NYMPreferredTrustIAndIIMember_0c871257-ce69-43a8-8749-0d0cb3b1fc0a_terseLabel_en-US" xlink:label="lab_adam_NYMPreferredTrustIAndIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust I And II</link:label>
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    <link:label id="lab_adam_NYMPreferredTrustIAndIIMember_documentation_en-US" xlink:label="lab_adam_NYMPreferredTrustIAndIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust I And II</link:label>
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    <link:label id="lab_dei_EntityShellCompany_d28ec1b3-1139-489d-816d-a5faed3c9986_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
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    <link:label id="lab_adam_ConsolidatedMortgageLoansMember_923072db-a539-4ac6-b298-1854ce10bece_terseLabel_en-US" xlink:label="lab_adam_ConsolidatedMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Mortgage Loans</link:label>
    <link:label id="lab_adam_ConsolidatedMortgageLoansMember_label_en-US" xlink:label="lab_adam_ConsolidatedMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Mortgage Loans [Member]</link:label>
    <link:label id="lab_adam_ConsolidatedMortgageLoansMember_documentation_en-US" xlink:label="lab_adam_ConsolidatedMortgageLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consolidated Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ConsolidatedMortgageLoansMember" xlink:href="adam-20251231.xsd#adam_ConsolidatedMortgageLoansMember"/>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_0dba9144-09ac-4713-9ecb-1ab629b3735c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRealEstateAccumulatedDepreciationRollForward_a63b4bd1-1cbd-463f-b1e5-3cd0e0aafedd_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfRealEstateAccumulatedDepreciationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Accumulated Depreciation for Operating Real Estate</link:label>
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    <link:label id="lab_adam_NonAgencyRMBSHeldInSecuritizationTrustMember_4940458b-8c0b-49e4-929e-c91e3c6aedaa_terseLabel_en-US" xlink:label="lab_adam_NonAgencyRMBSHeldInSecuritizationTrustMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non Agency RMBS Held In Securitization Trust</link:label>
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    <link:label id="lab_adam_NonAgencyRMBSHeldInSecuritizationTrustMember_documentation_en-US" xlink:label="lab_adam_NonAgencyRMBSHeldInSecuritizationTrustMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non Agency RMBS Held In Securitization Trust</link:label>
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    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_a3cad18e-a4c5-438b-b5b1-fa80ebd11eb6_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_OperatingSegmentsMember_019bf8a6-7dd6-74e9-bef9-5efa4a8f2eff_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
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    <link:label id="lab_adam_FinancingAndOtherVIEsMember_2369dc70-6a0a-4cd4-8c6f-b85ee3505c35_terseLabel_en-US" xlink:label="lab_adam_FinancingAndOtherVIEsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing And Other VIEs</link:label>
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    <link:label id="lab_adam_FinancingAndOtherVIEsMember_documentation_en-US" xlink:label="lab_adam_FinancingAndOtherVIEsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing And Other VIEs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingAndOtherVIEsMember" xlink:href="adam-20251231.xsd#adam_FinancingAndOtherVIEsMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019c2c55-0ab3-77d3-a932-ba480359d445_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked_22c069b6-a9f2-4388-9a04-3c75102d45f6_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked_label_en-US" xlink:label="lab_us-gaap_InterestIncomeSecuritiesMortgageBacked" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Securities, Mortgage-Backed</link:label>
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    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure_ab4c019f-e420-4569-901f-44e7e3c2fa25_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets in disposal group held for sale, estimated fair value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure_75843d2b-e960-4092-be76-0d8397b43260_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate in disposal group held for sale, estimated fair value</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure_label_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Long-Term Debt, Fair Value Disclosure</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure_documentation_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Long-Term Debt, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebtFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital_c13e5efb-c323-44ac-8783-e44ec9e27d15_terseLabel_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividend per share, return of capital (in dollars per share)</link:label>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital_label_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Taxable Dividend Per Share, Return Of Capital</link:label>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital_documentation_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Taxable Dividend Per Share, Return Of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:href="adam-20251231.xsd#adam_CommonStockTaxableDividendPerShareReturnOfCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:to="lab_adam_CommonStockTaxableDividendPerShareReturnOfCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseOperating_00894b2b-3385-4849-ad53-9b1cb7092bdb_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_1bec7647-839f-4918-993a-6769a1837b36_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_c44eb697-0193-42d7-9ede-957fa4b3f061_totalLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseOperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseOperating" xlink:to="lab_us-gaap_InterestExpenseOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UnrealizedGainLossOnDebt_74750ed8-8743-4e35-b237-2efc609861f7_negatedTerseLabel_en-US" xlink:label="lab_adam_UnrealizedGainLossOnDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized loss on debt</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnDebt_label_en-US" xlink:label="lab_adam_UnrealizedGainLossOnDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Debt</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnDebt_documentation_en-US" xlink:label="lab_adam_UnrealizedGainLossOnDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnrealizedGainLossOnDebt" xlink:href="adam-20251231.xsd#adam_UnrealizedGainLossOnDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnrealizedGainLossOnDebt" xlink:to="lab_adam_UnrealizedGainLossOnDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PreferredEquityDistributionAgreementMember_5df1de6c-a97e-4cbf-8471-f4fd1d9eade6_terseLabel_en-US" xlink:label="lab_adam_PreferredEquityDistributionAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Equity Distribution Agreement</link:label>
    <link:label id="lab_adam_PreferredEquityDistributionAgreementMember_label_en-US" xlink:label="lab_adam_PreferredEquityDistributionAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Equity Distribution Agreement [Member]</link:label>
    <link:label id="lab_adam_PreferredEquityDistributionAgreementMember_documentation_en-US" xlink:label="lab_adam_PreferredEquityDistributionAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Equity Distribution Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredEquityDistributionAgreementMember" xlink:href="adam-20251231.xsd#adam_PreferredEquityDistributionAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PreferredEquityDistributionAgreementMember" xlink:to="lab_adam_PreferredEquityDistributionAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivables_02b26894-cb91-4d66-af72-f0430447a59d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other receivables</link:label>
    <link:label id="lab_us-gaap_OtherReceivables_label_en-US" xlink:label="lab_us-gaap_OtherReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivables" xlink:to="lab_us-gaap_OtherReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_TX_2c5ca707-03dd-474b-9afc-ffefec70bae8_terseLabel_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Texas</link:label>
    <link:label id="lab_stpr_TX_label_en-US" xlink:label="lab_stpr_TX" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">TEXAS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_TX" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_TX"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_TX" xlink:to="lab_stpr_TX" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DebtSecuritiesAvailableForSaleWriteDown_019c4dfb-4966-7101-94c6-8bc692ed2986_terseLabel_en-US" xlink:label="lab_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized loss on write-downs</link:label>
    <link:label id="lab_adam_DebtSecuritiesAvailableForSaleWriteDown_label_en-US" xlink:label="lab_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available For Sale, Write-Down</link:label>
    <link:label id="lab_adam_DebtSecuritiesAvailableForSaleWriteDown_documentation_en-US" xlink:label="lab_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Available For Sale, Write-Down</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:href="adam-20251231.xsd#adam_DebtSecuritiesAvailableForSaleWriteDown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:to="lab_adam_DebtSecuritiesAvailableForSaleWriteDown" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PalmsAtCapeCoralLLCMember_a0442b6f-c931-409b-8c06-8c4864cb5d86_terseLabel_en-US" xlink:label="lab_adam_PalmsAtCapeCoralLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Palms at Cape Coral, LLC</link:label>
    <link:label id="lab_adam_PalmsAtCapeCoralLLCMember_label_en-US" xlink:label="lab_adam_PalmsAtCapeCoralLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Palms at Cape Coral, LLC [Member]</link:label>
    <link:label id="lab_adam_PalmsAtCapeCoralLLCMember_documentation_en-US" xlink:label="lab_adam_PalmsAtCapeCoralLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Palms at Cape Coral, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PalmsAtCapeCoralLLCMember" xlink:href="adam-20251231.xsd#adam_PalmsAtCapeCoralLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PalmsAtCapeCoralLLCMember" xlink:to="lab_adam_PalmsAtCapeCoralLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_6ac9901b-1638-4c06-aad3-e0df7d4baded_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate_2772f675-b8bd-49a0-a19e-237effab7acb_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Rate</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_6201ff14-e727-441f-9d69-a4ef23b15c63_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativesFairValueLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativesFairValueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Fair Value [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesFairValueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativesFairValueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesFairValueLineItems" xlink:to="lab_us-gaap_DerivativesFairValueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialAssetsLessthan90daysMember_64fbd86c-303c-4dd5-af28-3447e0ab6e6c_terseLabel_en-US" xlink:label="lab_adam_FinancialAssetsLessthan90daysMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 90 days past due</link:label>
    <link:label id="lab_adam_FinancialAssetsLessthan90daysMember_label_en-US" xlink:label="lab_adam_FinancialAssetsLessthan90daysMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Assets, Less than 90 days [Member]</link:label>
    <link:label id="lab_adam_FinancialAssetsLessthan90daysMember_documentation_en-US" xlink:label="lab_adam_FinancialAssetsLessthan90daysMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Assets, Less than 90 days [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialAssetsLessthan90daysMember" xlink:href="adam-20251231.xsd#adam_FinancialAssetsLessthan90daysMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialAssetsLessthan90daysMember" xlink:to="lab_adam_FinancialAssetsLessthan90daysMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember_393bb47b-45ea-4843-be14-9be13a6a887a_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Loans, Real Estate Owned And Single-Family Rental Properties</link:label>
    <link:label id="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember_label_en-US" xlink:label="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loans, Real Estate Owned And Single-Family Rental Properties [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans, Real Estate Owned And Single-Family Rental Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:to="lab_adam_ResidentialLoansRealEstateOwnedAndSingleFamilyRentalPropertiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AdvancedRemittancesFromResidentialLoanServicers_0b6e7931-d9bb-45b1-91dc-a900d7320999_terseLabel_en-US" xlink:label="lab_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advanced remittances from residential loan servicers</link:label>
    <link:label id="lab_adam_AdvancedRemittancesFromResidentialLoanServicers_label_en-US" xlink:label="lab_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Advanced Remittances From Residential Loan Servicers</link:label>
    <link:label id="lab_adam_AdvancedRemittancesFromResidentialLoanServicers_documentation_en-US" xlink:label="lab_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Advanced Remittances From Residential Loan Servicers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:href="adam-20251231.xsd#adam_AdvancedRemittancesFromResidentialLoanServicers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:to="lab_adam_AdvancedRemittancesFromResidentialLoanServicers" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_5451fc82-6220-4228-b327-962e7aa67fca_terseLabel_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and Fixtures</link:label>
    <link:label id="lab_us-gaap_FurnitureAndFixturesMember_label_en-US" xlink:label="lab_us-gaap_FurnitureAndFixturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Fixtures [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FurnitureAndFixturesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FurnitureAndFixturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FurnitureAndFixturesMember" xlink:to="lab_us-gaap_FurnitureAndFixturesMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfDividendsPayableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDividendsPayableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Dividends Payable [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_019bf84d-4f6a-7b2b-ba92-b5ac672620cb_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Business Combination Pro Forma Information</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueOtherChangesInFairValue"/>
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    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_5e67cb87-33fd-433d-9675-575dc1a4c123_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Based Compensation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
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    <link:label id="lab_dei_TradingSymbol_18a064a7-068d-4801-93a9-5ebfe2c534de_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_f84efb28-db34-4813-80b8-fe1c54de6199_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_019b9206-ebfa-78da-84a0-3e9b9932f6f3_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
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    <link:label id="lab_adam_A9.875SeniorNotesDue2030Member_019b06d9-ab0a-7649-adee-a67cabda86e2_terseLabel_en-US" xlink:label="lab_adam_A9.875SeniorNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">9.875% Senior Notes due 2030</link:label>
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    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateGainsLossesOnMortgageBankingActivitiesNet_019c41e9-1964-716e-bd09-34e333353087_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateGainsLossesOnMortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains/losses on mortgage banking activities, net</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_882c4240-0c08-41f4-8057-c71a80ab8beb_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in valuation allowance (as a percent)</link:label>
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    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredResidentialMortgageLoans_019bf84d-4f6a-7665-9c5c-76c1ff34e153_terseLabel_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredResidentialMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredStockRedemptionPeriod" xlink:href="adam-20251231.xsd#adam_PreferredStockRedemptionPeriod"/>
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    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_6a45a73d-0a93-4d8c-9eac-36694b0caf3d_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities in consolidated multi-family properties</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
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    <link:label id="lab_adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable_5b34b869-ea2a-4af7-9bcc-41b56628418b_terseLabel_en-US" xlink:label="lab_adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collections receivable from residential loan servicers</link:label>
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    <link:label id="lab_adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable_documentation_en-US" xlink:label="lab_adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, After Allowance For Credit Loss, Collections Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable" xlink:href="adam-20251231.xsd#adam_FinancingReceivableAfterAllowanceForCreditLossCollectionsReceivable"/>
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    <link:label id="lab_dei_EntityAddressCityOrTown_b24338a7-b667-408e-bc26-af33481eafbc_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_1fd8e925-5238-4e74-b5f9-28243bdc7ed2_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_51cbe33c-bb9c-4093-bdc0-67f1501862e2_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax assets</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net of Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNet" xlink:to="lab_us-gaap_DeferredTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_4e9c712f-8b39-4737-bd8b-d038b428d63c_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciationRealEstateSold_1dde6d23-8051-4c37-b817-b6c7e969a76f_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciationRealEstateSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification to held for sale or disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciationRealEstateSold_label_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciationRealEstateSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Accumulated Depreciation, Investment in Real Estate Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAccumulatedDepreciationRealEstateSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAccumulatedDepreciationRealEstateSold"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock_ace70854-e091-40c1-bff0-58d2934363ee_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements, Maturities</link:label>
    <link:label id="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock_label_en-US" xlink:label="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule Of Repurchase Agreements, Maturities [Table Text Block]</link:label>
    <link:label id="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock_documentation_en-US" xlink:label="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule Of Repurchase Agreements, Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:to="lab_adam_ScheduleOfRepurchaseAgreementsMaturitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_f72a471b-7c7a-4477-8d60-a21c73557b40_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_da461e62-63a9-4da0-885a-ead2f286908a_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights_d3366ea9-3303-4e98-9bcd-aabfb3a85a0f_terseLabel_en-US" xlink:label="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum number of quarters without dividends that result in voting rights</link:label>
    <link:label id="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights_label_en-US" xlink:label="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum Number of Quarters with No Dividends that Results in Voting Rights</link:label>
    <link:label id="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights_documentation_en-US" xlink:label="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Minimum Number of Quarters with No Dividends that Results in Voting Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:href="adam-20251231.xsd#adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:to="lab_adam_MinimumNumberofQuarterswithNoDividendsthatResultsinVotingRights" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_0217445c-d56c-4efc-8b2e-5124e009d6ca_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred loan fees, net</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_efc868ee-9c53-40fb-9db7-a512f1c9300c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net Deferred Finance Cost</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_547a7d89-e84c-4061-9105-a9be41dfa841_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash included in other assets</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_552d4096-aad5-419b-929a-2ecb4973a033_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_8bfed8a2-f510-484c-bca8-897f9400056c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_58570283-98aa-451c-a595-a8a8a2a37824_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubordinatedBorrowingNameDomain_8cdfe17c-8758-40cb-8c17-11e845d9d60f_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedBorrowingNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated Borrowing, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_SubordinatedBorrowingNameDomain_label_en-US" xlink:label="lab_us-gaap_SubordinatedBorrowingNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Borrowing, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedBorrowingNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedBorrowingNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedBorrowingNameDomain" xlink:to="lab_us-gaap_SubordinatedBorrowingNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_InterestIncomeAbstract_4a55fc5d-7725-4c0f-9820-7e71b79f3ce3_terseLabel_en-US" xlink:label="lab_adam_InterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NET INTEREST INCOME:</link:label>
    <link:label id="lab_adam_InterestIncomeAbstract_label_en-US" xlink:label="lab_adam_InterestIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">INTEREST INCOME:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSalesOfLoansNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSalesOfLoansNet"/>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateOriginalLoanAmountAxis_d045b75b-a197-4c8d-a12f-3c258f29dca4_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateOriginalLoanAmountAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Original Amount [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateOriginalLoanAmountAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateOriginalLoanAmountAxis"/>
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    <link:label id="lab_stpr_TN_56bfe960-33c9-4976-9109-921b3ed3ffc0_terseLabel_en-US" xlink:label="lab_stpr_TN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tennessee</link:label>
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    <link:label id="lab_adam_A2026SeniorNotesMember_2755d434-aee1-4cbc-b688-3f6c7135fb9b_terseLabel_en-US" xlink:label="lab_adam_A2026SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 Senior Notes</link:label>
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    <link:label id="lab_adam_A2026SeniorNotesMember_documentation_en-US" xlink:label="lab_adam_A2026SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2026 Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A2026SeniorNotesMember" xlink:href="adam-20251231.xsd#adam_A2026SeniorNotesMember"/>
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    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement_40aa59eb-2138-45a4-adef-18c8659c3027_negatedTerseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer to SFR</link:label>
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    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement_documentation_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Stable Funding Requirement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement" xlink:href="adam-20251231.xsd#adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateStableFundingRequirement"/>
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    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_019c2cc3-50be-75a9-8b8f-7a580d4631a1_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease in the valuation allowance for the current year</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount"/>
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    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements_e423a37c-0665-455f-8b1d-aaafeb3ffbad_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Buildings and Improvements</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Initial Cost of Building and Improvements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements" xlink:to="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfBuildingsAndImprovements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_019b923d-fb6b-7c2d-8878-b82180106a0f_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of residential loans</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfNotesReceivable_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Financing Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfNotesReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:to="lab_us-gaap_GainLossOnSaleOfNotesReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
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    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019bf84d-4f6a-7c3e-9553-c7ea2ee33a65_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Estimated Amortization Expense Related to the Acquired Identifiable Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_98a7b1c2-6981-47df-b038-37c4f98c43fd_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward_2bdd684c-0945-44b7-b3ff-daef22b3cade_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Non-vested Restricted Shares</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedRollForward"/>
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    <link:label id="lab_us-gaap_PledgedStatusDomain_019b07d9-26b4-7778-9c5b-43fd0ecad8e9_terseLabel_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:label id="lab_us-gaap_PledgedStatusDomain_label_en-US" xlink:label="lab_us-gaap_PledgedStatusDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pledged Status [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PledgedStatusDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PledgedStatusDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PledgedStatusDomain" xlink:to="lab_us-gaap_PledgedStatusDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ConsolidatedRealEstateMember_27fd5a06-e470-4d3f-8883-1cbde067d9ab_terseLabel_en-US" xlink:label="lab_adam_ConsolidatedRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Real Estate</link:label>
    <link:label id="lab_adam_ConsolidatedRealEstateMember_label_en-US" xlink:label="lab_adam_ConsolidatedRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Real Estate [Member]</link:label>
    <link:label id="lab_adam_ConsolidatedRealEstateMember_documentation_en-US" xlink:label="lab_adam_ConsolidatedRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Consolidated Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ConsolidatedRealEstateMember" xlink:href="adam-20251231.xsd#adam_ConsolidatedRealEstateMember"/>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_e6e6c162-a0e1-489d-a1f6-099a96dea69b_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
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    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
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    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_2d214868-000b-46db-a4a3-2650ed71d9c6_verboseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment securities available for sale</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeSecurities_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Securities, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeSecurities" xlink:to="lab_us-gaap_InterestAndDividendIncomeSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_2ff962a0-253d-4dc9-88fa-3cf8d5c5b278_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_28b67e74-f048-4206-b422-1fa46e333811_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income tax provision</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_a0da0a52-44bd-491c-a7ba-bfe98474850c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax (benefit) expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_BOrBelowCreditRatingMember_8424dbf4-8a47-48eb-ab77-50fe1add540a_terseLabel_en-US" xlink:label="lab_adam_BOrBelowCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">B+ Or Below Credit Rating</link:label>
    <link:label id="lab_adam_BOrBelowCreditRatingMember_label_en-US" xlink:label="lab_adam_BOrBelowCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">B+ Or Below Credit Rating [Member]</link:label>
    <link:label id="lab_adam_BOrBelowCreditRatingMember_documentation_en-US" xlink:label="lab_adam_BOrBelowCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">B+ Or Below Credit Rating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BOrBelowCreditRatingMember" xlink:href="adam-20251231.xsd#adam_BOrBelowCreditRatingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_BOrBelowCreditRatingMember" xlink:to="lab_adam_BOrBelowCreditRatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1_8f68e411-19ca-4f48-a9ea-9c446711a808_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciable Period (Years)</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Life Used for Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1" xlink:to="lab_us-gaap_RealEstateAndAccumulatedDepreciationLifeUsedForDepreciation1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_d6797569-a3ab-4465-a224-c69fa955e528_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Spread on variable interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019b8cba-eec5-751d-b54e-b994bfbdc21c_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_5bd00063-c9d2-4ab5-8b74-34e4beccab79_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_294bfd1c-5e5e-4d79-bf08-ef1ba209b869_totalLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember_019c4dfe-66e0-7e1f-96f5-8fb15f6a92d6_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Two Multi-Family Apartment Communities</link:label>
    <link:label id="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember_label_en-US" xlink:label="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Two Multi-Family Apartment Communities [Member]</link:label>
    <link:label id="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember_documentation_en-US" xlink:label="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Two Multi-Family Apartment Communities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:href="adam-20251231.xsd#adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:to="lab_adam_DisposalGroupTwoMultiFamilyApartmentCommunitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_c4513b4b-3993-40cc-826c-976a0e2ba650_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_60d40451-67b8-475c-bb0f-95dca349d352_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at the end of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale_019c40bd-be9b-7305-b9b9-5ec5fb22e7f6_terseLabel_en-US" xlink:label="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal balance of loans repurchased</link:label>
    <link:label id="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment For Repurchase Of Mortgage Loans Held-For-Sale</link:label>
    <link:label id="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale_documentation_en-US" xlink:label="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment For Repurchase Of Mortgage Loans Held-For-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:href="adam-20251231.xsd#adam_PaymentForRepurchaseOfMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:to="lab_adam_PaymentForRepurchaseOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_087b61b4-39f9-4610-8130-08934b43f529_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetMeasurementInput_d2aec3eb-5165-4f8e-95b5-40638d54a122_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing asset, measurement input</link:label>
    <link:label id="lab_us-gaap_ServicingAssetMeasurementInput_label_en-US" xlink:label="lab_us-gaap_ServicingAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetMeasurementInput" xlink:to="lab_us-gaap_ServicingAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_f8b8c70e-e90b-4e05-94a6-9cc742d41824_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnsecuredDebt_7654ae93-292b-4d39-9b08-86fa75d4c736_terseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes ($260,852 at fair value and $99,585 at amortized cost, net as of December&#160;31, 2025 and $60,310 at fair value and $98,886 at amortized cost, net as of December&#160;31, 2024)</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_0728d757-3387-4667-951b-5569730e69cd_verboseLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_ae78c4ba-2ddc-42f8-9fe4-e1432c4c10d7_netLabel_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes, carrying value</link:label>
    <link:label id="lab_us-gaap_UnsecuredDebt_label_en-US" xlink:label="lab_us-gaap_UnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnsecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnsecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnsecuredDebt" xlink:to="lab_us-gaap_UnsecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PerformanceSharesTargetMember_87859272-d82f-41bc-ac27-7fa05ac4242c_terseLabel_en-US" xlink:label="lab_adam_PerformanceSharesTargetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PSUs, Target</link:label>
    <link:label id="lab_adam_PerformanceSharesTargetMember_label_en-US" xlink:label="lab_adam_PerformanceSharesTargetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Shares, Target [Member]</link:label>
    <link:label id="lab_adam_PerformanceSharesTargetMember_documentation_en-US" xlink:label="lab_adam_PerformanceSharesTargetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Shares, Target</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PerformanceSharesTargetMember" xlink:href="adam-20251231.xsd#adam_PerformanceSharesTargetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PerformanceSharesTargetMember" xlink:to="lab_adam_PerformanceSharesTargetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember_f398def8-da60-48a1-b65e-6079b9b46d39_verboseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held in securitization trusts</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember_1368db2b-ddc4-489e-b80c-8fe9f9f65a1a_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held in securitization trusts</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans Held In Securitization Trust, At Fair Value [Member]</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans Held In Securitization Trust, At Fair Value [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:to="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_6f1348c2-d064-4fad-ac0e-abb4f9bb0537_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement_7173cdf2-24db-4580-ad5f-10c3cc4cad36_terseLabel_en-US" xlink:label="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of joint venture entities with debt restructuring agreement</link:label>
    <link:label id="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement_label_en-US" xlink:label="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Joint Venture Entities With Debt Restructuring Agreement</link:label>
    <link:label id="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement_documentation_en-US" xlink:label="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Joint Venture Entities With Debt Restructuring Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:href="adam-20251231.xsd#adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:to="lab_adam_NumberOfJointVentureEntitiesWithDebtRestructuringAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember_019c28b9-20a0-7fe9-ab1e-31eb16efd9dc_terseLabel_en-US" xlink:label="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs and DSUs</link:label>
    <link:label id="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember_label_en-US" xlink:label="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Deferred Stock Units [Member]</link:label>
    <link:label id="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember_documentation_en-US" xlink:label="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Stock Units And Deferred Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:href="adam-20251231.xsd#adam_RestrictedStockUnitsAndDeferredStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:to="lab_adam_RestrictedStockUnitsAndDeferredStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OffsettingAbstract_label_en-US" xlink:label="lab_us-gaap_OffsettingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Offsetting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OffsettingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OffsettingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OffsettingAbstract" xlink:to="lab_us-gaap_OffsettingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RepurchasesOfResidentialLoans_019c222d-e4be-7676-9ed0-57211d086b55_negatedTerseLabel_en-US" xlink:label="lab_adam_RepurchasesOfResidentialLoans" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchases of residential loans</link:label>
    <link:label id="lab_adam_RepurchasesOfResidentialLoans_label_en-US" xlink:label="lab_adam_RepurchasesOfResidentialLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchases of Residential Loans</link:label>
    <link:label id="lab_adam_RepurchasesOfResidentialLoans_documentation_en-US" xlink:label="lab_adam_RepurchasesOfResidentialLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchases of Residential Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RepurchasesOfResidentialLoans" xlink:href="adam-20251231.xsd#adam_RepurchasesOfResidentialLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RepurchasesOfResidentialLoans" xlink:to="lab_adam_RepurchasesOfResidentialLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentTable_877667c1-3a7b-4670-909d-6edfc1c4375d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment [Table]</link:label>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentTable_label_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermPurchaseCommitmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermPurchaseCommitmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermPurchaseCommitmentTable" xlink:to="lab_us-gaap_LongTermPurchaseCommitmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_479e234f-d272-488d-9e82-4a7eb0810e29_terseLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing fees</link:label>
    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount_label_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contractually Specified Servicing Fees, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractuallySpecifiedServicingFeesAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:to="lab_us-gaap_ContractuallySpecifiedServicingFeesAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DerivativePaymentTypeDomain_385f60ca-cec1-4f2a-8619-6a57c912e773_terseLabel_en-US" xlink:label="lab_adam_DerivativePaymentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Payment Type [Domain]</link:label>
    <link:label id="lab_adam_DerivativePaymentTypeDomain_label_en-US" xlink:label="lab_adam_DerivativePaymentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Payment Type [Domain]</link:label>
    <link:label id="lab_adam_DerivativePaymentTypeDomain_documentation_en-US" xlink:label="lab_adam_DerivativePaymentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Payment Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DerivativePaymentTypeDomain" xlink:href="adam-20251231.xsd#adam_DerivativePaymentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DerivativePaymentTypeDomain" xlink:to="lab_adam_DerivativePaymentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ReceivablesAndOtherAssetsFairValue_fddb1d55-14a3-4c36-b573-a4ef9d4b9897_terseLabel_en-US" xlink:label="lab_adam_ReceivablesAndOtherAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family loans, estimated fair value</link:label>
    <link:label id="lab_adam_ReceivablesAndOtherAssetsFairValue_label_en-US" xlink:label="lab_adam_ReceivablesAndOtherAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables And Other Assets Fair Value</link:label>
    <link:label id="lab_adam_ReceivablesAndOtherAssetsFairValue_documentation_en-US" xlink:label="lab_adam_ReceivablesAndOtherAssetsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents fair value disclosure for receivables and other assets.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ReceivablesAndOtherAssetsFairValue" xlink:href="adam-20251231.xsd#adam_ReceivablesAndOtherAssetsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ReceivablesAndOtherAssetsFairValue" xlink:to="lab_adam_ReceivablesAndOtherAssetsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember_019b0825-ab1e-78e8-9c49-08b605dedef1_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Held-for-Sale</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Held-for-Sale [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsHeldforsaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:to="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DividendsDeclaredButNotYetPaid_019b0722-2202-7ed4-84bb-73b8f6ec4c40_terseLabel_en-US" xlink:label="lab_adam_DividendsDeclaredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends and dividend equivalents payable</link:label>
    <link:label id="lab_adam_DividendsDeclaredButNotYetPaid_label_en-US" xlink:label="lab_adam_DividendsDeclaredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Declared But Not Yet Paid</link:label>
    <link:label id="lab_adam_DividendsDeclaredButNotYetPaid_documentation_en-US" xlink:label="lab_adam_DividendsDeclaredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Dividends Declared But Not Yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DividendsDeclaredButNotYetPaid" xlink:href="adam-20251231.xsd#adam_DividendsDeclaredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DividendsDeclaredButNotYetPaid" xlink:to="lab_adam_DividendsDeclaredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SingleFamilyMember_47541543-04c2-4763-a7af-5c04f5144a61_terseLabel_en-US" xlink:label="lab_srt_SingleFamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single-Family Rental - Operating</link:label>
    <link:label id="lab_srt_SingleFamilyMember_label_en-US" xlink:label="lab_srt_SingleFamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single Family [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SingleFamilyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SingleFamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SingleFamilyMember" xlink:to="lab_srt_SingleFamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock_8b01a67e-7cb8-4441-bf99-a1174992c795_terseLabel_en-US" xlink:label="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Net Gain (Loss) on Residential Mortgage Loans at Fair Value</link:label>
    <link:label id="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock_label_en-US" xlink:label="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components Of Net Gains (Losses) On Residential Mortgage Loans At Fair Value [Table Text Block]</link:label>
    <link:label id="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock_documentation_en-US" xlink:label="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Components Of Net Gains (Losses) On Residential Mortgage Loans At Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:href="adam-20251231.xsd#adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:to="lab_adam_ComponentsOfNetGainsLossesOnResidentialMortgageLoansAtFairValueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive_019be4fe-3f8a-7e51-96b6-900496f340ce_terseLabel_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MSRs acquired through business combination</link:label>
    <link:label id="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive_label_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights Received From The Acquisition of Constructive</link:label>
    <link:label id="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive_documentation_en-US" xlink:label="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights Received From The Acquisition of Constructive</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:href="adam-20251231.xsd#adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:to="lab_adam_MortgageServicingRightsReceivedFromTheAcquisitionOfConstructive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment_f9fbf573-6910-40d9-a0ae-e2581d4ab8ea_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from securitizations of loans held-for-investment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Securitization, Loan, Held-for-Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:to="lab_us-gaap_ProceedsFromSecuritizationsOfLoansHeldForInvestment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionTableTextBlock_05594e60-e66e-4add-b4a0-0a20f1f9811d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt Instrument Redemption</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionTableTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument Redemption [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:to="lab_us-gaap_DebtInstrumentRedemptionTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncomeAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OtherIncomeAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncomeAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncomeAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncomeAndExpensesAbstract" xlink:to="lab_us-gaap_OtherIncomeAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_019c2248-ec4d-705d-8ae7-1e84fbc3f51a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of businesses, net of cash and restricted cash acquired</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_3230808b-2b8d-407e-b18e-cdd5f594d95d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, redemption price, percentage</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome_16f87d25-838b-4103-912c-bef4a47c9745_negatedLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Non-taxable REIT (income) loss (as a percent)</link:label>
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    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_63be904e-f7e1-43fd-a58d-05d6fa872405_negatedLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Preferred stock dividends</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_4525dbcc-0369-49d9-95e6-97ff4e4cf9af_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationOtherAdjustments"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR_491aa8f5-1650-406c-97ab-60d7688e8610_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMortgageServicingRightsMSR" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of mortgage servicing rights</link:label>
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    <link:label id="lab_us-gaap_InvestmentCompanyDistributableEarningsLossAccumulatedLongTermCapitalGainLoss_36cc7d32-0fd5-4325-bd9e-67d55d2e0b31_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributableEarningsLossAccumulatedLongTermCapitalGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital losses</link:label>
    <link:label id="lab_us-gaap_InvestmentCompanyDistributableEarningsLossAccumulatedLongTermCapitalGainLoss_label_en-US" xlink:label="lab_us-gaap_InvestmentCompanyDistributableEarningsLossAccumulatedLongTermCapitalGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Company, Distributable Earnings (Loss), Accumulated Long-Term Capital Gain (Loss)</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesAbstract_2eb3bf8f-02da-4dc2-b8c0-c657b12ba3cb_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesAbstract"/>
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    <link:label id="lab_adam_ColliervilleTNMember_4cccd2e8-9e39-42e6-8507-41cd7a404520_terseLabel_en-US" xlink:label="lab_adam_ColliervilleTNMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collierville, TN</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_8157e2f4-de14-40f5-90bd-c64bc2fd59df_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares outstanding, unvested restricted stock (in shares)</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_a3dcb6e1-7a31-4ac9-ba7a-f3ede233d870_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_9f135343-dac3-4041-a68f-92066738478b_netLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Investment securities available for sale, at fair value</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest_4f8ebf2d-f89a-4c55-bd71-cd18a1b4505a_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleExcludingAccruedInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Investment securities available for sale:</link:label>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_fa8ec1ec-f17a-45bd-a2ec-804114d1146e_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Sales</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_1091c886-3efb-4ba5-99ff-ed1efaa4197c_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment useful life</link:label>
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    <link:label id="lab_us-gaap_BuildingImprovementsMember_1e824a1e-9d55-4019-9859-8510d0a75c9b_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building Improvements</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingImprovementsMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
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    <link:label id="lab_us-gaap_InterestIncomeExpenseNet_5432ad38-2f4a-4064-891d-ce1b8540e234_totalLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total net interest income</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_a3d11346-87f8-49b3-9279-a918154fb5fd_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1_019c2251-4b48-7a26-8fa7-43c2b9a63d6c_terseLabel_en-US" xlink:label="lab_us-gaap_TransferOfLoansHeldForSaleToPortfolioLoans1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer from residential loans held for sale to residential loans</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_6c836bea-a0a1-435b-9129-9be9588b3af0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">April&#160;30, 2024 - April&#160;29, 2025</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis_47ffe18b-ede8-49a0-baa2-85511c496f5e_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities or Other Assets Sold under Agreements to Repurchase, Maturity Periods [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements and Similar Transactions, Maturity Periods [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_56a0358a-7f50-47a5-8125-125d4896b616_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gross Amount of Recognized Assets (Liabilities)</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiability_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, before Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_098fa373-bd52-4983-a17a-a9731b935853_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestChangeInRedemptionValue_5a0cb887-4c72-4b63-8535-c32056eef5ac_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment of redeemable non-controlling interest to estimated redemption value</link:label>
    <link:label id="lab_us-gaap_MinorityInterestChangeInRedemptionValue_label_en-US" xlink:label="lab_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Change in Redemption Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestChangeInRedemptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:to="lab_us-gaap_MinorityInterestChangeInRedemptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FreddieMacMember_38563050-f283-4365-9955-15c7f6da6ff9_terseLabel_en-US" xlink:label="lab_adam_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:label id="lab_adam_FreddieMacMember_label_en-US" xlink:label="lab_adam_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Freddie Mac [Member]</link:label>
    <link:label id="lab_adam_FreddieMacMember_documentation_en-US" xlink:label="lab_adam_FreddieMacMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Freddie Mac</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FreddieMacMember" xlink:href="adam-20251231.xsd#adam_FreddieMacMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FreddieMacMember" xlink:to="lab_adam_FreddieMacMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_d630f906-e9de-411e-aa34-5aabe68d34b3_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAbstract_019be4fe-3f8a-7526-84dd-b8e18b077620_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in fair value due to:</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAbstract_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAbstract" xlink:to="lab_us-gaap_ServicingAssetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount_14a6ef22-5c73-49e2-968a-2b5fababb39e_terseLabel_en-US" xlink:label="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepayment fees</link:label>
    <link:label id="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount_label_en-US" xlink:label="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepayment Fees On Servicing Financial Assets Amount</link:label>
    <link:label id="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount_documentation_en-US" xlink:label="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Prepayment Fees On Servicing Financial Assets Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:href="adam-20251231.xsd#adam_PrepaymentFeesOnServicingFinancialAssetsAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:to="lab_adam_PrepaymentFeesOnServicingFinancialAssetsAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndOtherIncome_038a710f-fdab-41b3-b0d8-0e8b2c0bb204_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndOtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndOtherIncome_label_en-US" xlink:label="lab_us-gaap_InterestAndOtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndOtherIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndOtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndOtherIncome" xlink:to="lab_us-gaap_InterestAndOtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity_edbcd7a9-9bd6-451b-ac2e-219cad5e52cd_terseLabel_en-US" xlink:label="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in non-controlling interest related to initial consolidation of VIEs</link:label>
    <link:label id="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity_label_en-US" xlink:label="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase in Noncontrolling Interest, Initial Consolidation of Variable Interest Entity</link:label>
    <link:label id="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity_documentation_en-US" xlink:label="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase in Noncontrolling Interest, Initial Consolidation of Variable Interest Entity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:href="adam-20251231.xsd#adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:to="lab_adam_IncreaseInNoncontrollingInterestInitialConsolidationOfVariableInterestEntity" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ExpensesRelatedToOperatingRealEstate_f35c1dc0-6981-4acf-b0c3-df7b138ca512_totalLabel_en-US" xlink:label="lab_adam_ExpensesRelatedToOperatingRealEstate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses related to real estate</link:label>
    <link:label id="lab_adam_ExpensesRelatedToOperatingRealEstate_d341f134-f19e-4ad5-be04-07255c602ab6_terseLabel_en-US" xlink:label="lab_adam_ExpensesRelatedToOperatingRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses related to real estate</link:label>
    <link:label id="lab_adam_ExpensesRelatedToOperatingRealEstate_label_en-US" xlink:label="lab_adam_ExpensesRelatedToOperatingRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Expenses Related To Operating Real Estate</link:label>
    <link:label id="lab_adam_ExpensesRelatedToOperatingRealEstate_documentation_en-US" xlink:label="lab_adam_ExpensesRelatedToOperatingRealEstate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Expenses Related To Operating Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ExpensesRelatedToOperatingRealEstate" xlink:href="adam-20251231.xsd#adam_ExpensesRelatedToOperatingRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ExpensesRelatedToOperatingRealEstate" xlink:to="lab_adam_ExpensesRelatedToOperatingRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_1ae875e9-67b6-4e2b-9b2a-4fa560fcf271_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock_888a31e9-618d-44ff-b031-5fd2b81f1cd3_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Realized Gain or Loss Activity</link:label>
    <link:label id="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock_label_en-US" xlink:label="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments Securities Sold [Table Text Block]</link:label>
    <link:label id="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock_documentation_en-US" xlink:label="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Investments Securities Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:to="lab_adam_ScheduleOfInvestmentsSecuritiesSoldTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_0fd8026e-9540-42d3-957b-f85f04f207f4_terseLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_24bd0293-461d-4283-85d8-1c898c33226c_totalLabel_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total interest income</link:label>
    <link:label id="lab_us-gaap_InterestAndDividendIncomeOperating_label_en-US" xlink:label="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Dividend Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestAndDividendIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestAndDividendIncomeOperating" xlink:to="lab_us-gaap_InterestAndDividendIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateOtherAcquisitions_8f28fa28-5416-4b23-946d-7933b66f4c96_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateOtherAcquisitions" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions</link:label>
    <link:label id="lab_us-gaap_RealEstateOtherAcquisitions_label_en-US" xlink:label="lab_us-gaap_RealEstateOtherAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Other Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateOtherAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateOtherAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateOtherAcquisitions" xlink:to="lab_us-gaap_RealEstateOtherAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_c19c50b8-1758-42cc-9f34-dd4e00e836f2_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Domain]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:to="lab_us-gaap_FinancingReceivablesPeriodPastDueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageLoansOver299999Member_0231317b-85d2-4eb5-894b-7147e48a6e4c_terseLabel_en-US" xlink:label="lab_adam_MortgageLoansOver299999Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans Over $299,999</link:label>
    <link:label id="lab_adam_MortgageLoansOver299999Member_label_en-US" xlink:label="lab_adam_MortgageLoansOver299999Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans Over $299,999 [Member]</link:label>
    <link:label id="lab_adam_MortgageLoansOver299999Member_documentation_en-US" xlink:label="lab_adam_MortgageLoansOver299999Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans Over $299,999</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageLoansOver299999Member" xlink:href="adam-20251231.xsd#adam_MortgageLoansOver299999Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MortgageLoansOver299999Member" xlink:to="lab_adam_MortgageLoansOver299999Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAsset_8ed08d77-b156-4b3e-9c96-faffd532c3be_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, carrying value</link:label>
    <link:label id="lab_us-gaap_ServicingAsset_label_en-US" xlink:label="lab_us-gaap_ServicingAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAsset" xlink:to="lab_us-gaap_ServicingAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_846c1d81-7c5d-4448-9bf8-0d3f2cdae057_terseLabel_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans receivable, at fair value</link:label>
    <link:label id="lab_us-gaap_LoansReceivableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Receivable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansReceivableFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansReceivableFairValueDisclosure" xlink:to="lab_us-gaap_LoansReceivableFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_019c653a-cfa3-7d69-a2e2-c68703603f0b_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost on employer contribution plan</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:to="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST_c042fa14-1c01-42a8-970e-c615c856414f_negatedTerseLabel_en-US" xlink:label="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of investments held in Consolidated SLST</link:label>
    <link:label id="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST_label_en-US" xlink:label="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Purchase Of Investments Held In Consolidated SLST</link:label>
    <link:label id="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST_documentation_en-US" xlink:label="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Purchase Of Investments Held In Consolidated SLST</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:href="adam-20251231.xsd#adam_PurchaseOfInvestmentsHeldInConsolidatedSLST"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:to="lab_adam_PurchaseOfInvestmentsHeldInConsolidatedSLST" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries_bda9ae51-6066-49f0-af60-102393a5e63f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds from sale of real estate</link:label>
    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries_label_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Divestiture of Interest in Consolidated Subsidiaries</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries" xlink:to="lab_us-gaap_ProceedsFromDivestitureOfInterestInConsolidatedSubsidiaries" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_7ba0b603-8ab6-4fd4-b7cc-1ba01f098f60_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Dividends paid on common stock and dividend equivalents</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_1528bd95-7d8b-4976-a271-54dcce98f7cd_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation_8bfad959-4c0e-4733-af54-c8b3a086e973_terseLabel_en-US" xlink:label="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain (losses) recognized on CDOs</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation_label_en-US" xlink:label="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Collateralized Debt Obligation</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation_documentation_en-US" xlink:label="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Collateralized Debt Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:href="adam-20251231.xsd#adam_UnrealizedGainLossOnCollateralizedDebtObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:to="lab_adam_UnrealizedGainLossOnCollateralizedDebtObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember_019b06f8-abae-70d0-bf48-ebcbe7af9c5b_verboseLabel_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations, at fair value</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember_06b6897c-bebb-4364-a2b8-5d5b71dab767_terseLabel_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated SLST</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember_label_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Collateralized Debt Obligations, At Fair Value [Member]</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember_documentation_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Collateralized Debt Obligations, At Fair Value [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:href="adam-20251231.xsd#adam_ResidentialCollateralizedDebtObligationsAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:to="lab_adam_ResidentialCollateralizedDebtObligationsAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RealEstateOwnedTransferToRealEstateNet_9a3dd8d5-a1a4-41f1-a83a-daeb61c861bf_terseLabel_en-US" xlink:label="lab_adam_RealEstateOwnedTransferToRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer from residential loans to real estate, net</link:label>
    <link:label id="lab_adam_RealEstateOwnedTransferToRealEstateNet_label_en-US" xlink:label="lab_adam_RealEstateOwnedTransferToRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Net</link:label>
    <link:label id="lab_adam_RealEstateOwnedTransferToRealEstateNet_documentation_en-US" xlink:label="lab_adam_RealEstateOwnedTransferToRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned, Transfer to Real Estate Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateOwnedTransferToRealEstateNet" xlink:href="adam-20251231.xsd#adam_RealEstateOwnedTransferToRealEstateNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RealEstateOwnedTransferToRealEstateNet" xlink:to="lab_adam_RealEstateOwnedTransferToRealEstateNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_TotalOperatingRealEstateMember_dab2688d-9b52-4f34-a4b4-494e3160b9a6_terseLabel_en-US" xlink:label="lab_adam_TotalOperatingRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate</link:label>
    <link:label id="lab_adam_TotalOperatingRealEstateMember_label_en-US" xlink:label="lab_adam_TotalOperatingRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate [Member]</link:label>
    <link:label id="lab_adam_TotalOperatingRealEstateMember_documentation_en-US" xlink:label="lab_adam_TotalOperatingRealEstateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_TotalOperatingRealEstateMember" xlink:href="adam-20251231.xsd#adam_TotalOperatingRealEstateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_TotalOperatingRealEstateMember" xlink:to="lab_adam_TotalOperatingRealEstateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_019c41c0-566c-792c-8003-9e4c8595f7e8_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repayments of debt</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLongTermDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepaymentsOfLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLongTermDebt" xlink:to="lab_us-gaap_RepaymentsOfLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_StepUpInterestRateOneMember_f6d9b1a6-ab6b-4043-af3d-963bf35df921_terseLabel_en-US" xlink:label="lab_adam_StepUpInterestRateOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate One</link:label>
    <link:label id="lab_adam_StepUpInterestRateOneMember_label_en-US" xlink:label="lab_adam_StepUpInterestRateOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate One [Member]</link:label>
    <link:label id="lab_adam_StepUpInterestRateOneMember_documentation_en-US" xlink:label="lab_adam_StepUpInterestRateOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_StepUpInterestRateOneMember" xlink:href="adam-20251231.xsd#adam_StepUpInterestRateOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_StepUpInterestRateOneMember" xlink:to="lab_adam_StepUpInterestRateOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_a3d56599-b751-4209-a563-b6aaf58c1e64_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember_feaa9fef-c03c-468c-98ab-5eedcabf5765_verboseLabel_en-US" xlink:label="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Preferred Equity and Mezzanine Loan Investments</link:label>
    <link:label id="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember_label_en-US" xlink:label="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mezzanine Loan And Preferred Equity Investments [Member]</link:label>
    <link:label id="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember_documentation_en-US" xlink:label="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mezzanine Loan and Preferred Equity Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:href="adam-20251231.xsd#adam_MezzanineLoanAndPreferredEquityInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:to="lab_adam_MezzanineLoanAndPreferredEquityInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations_2de268d6-bd4b-4a9c-9b8e-8e548632b1b7_terseLabel_en-US" xlink:label="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of collateralized debt obligations, net</link:label>
    <link:label id="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations_label_en-US" xlink:label="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Issuance of Collateralized Debt Obligations</link:label>
    <link:label id="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations_documentation_en-US" xlink:label="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Issuance of Collateralized Debt Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:href="adam-20251231.xsd#adam_ProceedsFromIssuanceOfCollateralizedDebtObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:to="lab_adam_ProceedsFromIssuanceOfCollateralizedDebtObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember_462823c7-9d27-4fd1-b914-f88d6db9b11e_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Loans Held in Consolidated SLST</link:label>
    <link:label id="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember_label_en-US" xlink:label="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loans Held in Consolidated SLST [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans Held in Consolidated SLST</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoansHeldInConsolidatedSLSTMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:to="lab_adam_ResidentialLoansHeldInConsolidatedSLSTMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock_4293227f-7089-4dd7-8faa-f6cac77225a5_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Loans and Residential Loans Held for Sale</link:label>
    <link:label id="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock_label_en-US" xlink:label="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loans And Residential Loans Held For Sale [Policy Text Block]</link:label>
    <link:label id="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock_documentation_en-US" xlink:label="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans And Residential Loans Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:href="adam-20251231.xsd#adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:to="lab_adam_ResidentialLoansAndResidentialLoansHeldForSalePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialMortgageLoansPastDuePeriod_dac4a034-99e4-44a3-9d6a-ef5fd1986872_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansPastDuePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential mortgage loans, past due period</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansPastDuePeriod_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansPastDuePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Past Due Period</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansPastDuePeriod_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansPastDuePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Past Due Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansPastDuePeriod" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansPastDuePeriod"/>
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    <link:label id="lab_us-gaap_GainLossOnSaleOfDerivatives_0f3edcd7-f531-487f-8857-cf60110442d6_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized Gains (Losses)</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfDerivatives_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfDerivatives"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfDerivatives" xlink:to="lab_us-gaap_GainLossOnSaleOfDerivatives" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_e7330c14-462e-4f6d-be54-4cc9fc7a7f84_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforward</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoanSecuritizationAtFairValueMember_b067b299-86c8-4b8d-8136-c6077bf251ae_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations at fair value</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationAtFairValueMember_label_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loan Securitization at Fair Value [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationAtFairValueMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loan Securitization at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoanSecuritizationAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:to="lab_adam_ResidentialLoanSecuritizationAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_a69c2b74-5abd-490c-b869-49f207590600_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RapidCityRMIJVLLCMember_9355c6a8-1493-41e3-a6da-cc4d025594d3_terseLabel_en-US" xlink:label="lab_adam_RapidCityRMIJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rapid City RMI JV LLC</link:label>
    <link:label id="lab_adam_RapidCityRMIJVLLCMember_label_en-US" xlink:label="lab_adam_RapidCityRMIJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rapid City RMI JV, LLC [Member]</link:label>
    <link:label id="lab_adam_RapidCityRMIJVLLCMember_documentation_en-US" xlink:label="lab_adam_RapidCityRMIJVLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rapid City RMI JV, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RapidCityRMIJVLLCMember" xlink:href="adam-20251231.xsd#adam_RapidCityRMIJVLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RapidCityRMIJVLLCMember" xlink:to="lab_adam_RapidCityRMIJVLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019be5a9-d5f8-73e0-9d1a-0c571498466d_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand_94049f1f-6269-453d-aa61-64ad013f074a_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Initial Cost of Land</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationInitialCostOfLand"/>
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    <link:label id="lab_adam_SeniorUnsecuredNotesAbstract_a7f4f604-c4b6-4c29-973f-604b0390eb94_terseLabel_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes:</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesAbstract_label_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes [Abstract]</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesAbstract_documentation_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SeniorUnsecuredNotesAbstract" xlink:href="adam-20251231.xsd#adam_SeniorUnsecuredNotesAbstract"/>
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    <link:label id="lab_us-gaap_ProceedsFromPaymentsToMinorityShareholders_e6fd073d-223d-4ac3-8428-42fa3216f987_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net distributions to non-controlling interests in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsToMinorityShareholders_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsToMinorityShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payments to) Noncontrolling Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsToMinorityShareholders" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsToMinorityShareholders"/>
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    <link:label id="lab_adam_OTHERINCOMEEXPENSEAbstract_d033b28a-17f7-4f42-bc4d-828e189d7013_terseLabel_en-US" xlink:label="lab_adam_OTHERINCOMEEXPENSEAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">OTHER INCOME (LOSS):</link:label>
    <link:label id="lab_adam_OTHERINCOMEEXPENSEAbstract_019c419f-9e5f-791c-8272-9cebaad133e7_verboseLabel_en-US" xlink:label="lab_adam_OTHERINCOMEEXPENSEAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">OTHER INCOME:</link:label>
    <link:label id="lab_adam_OTHERINCOMEEXPENSEAbstract_label_en-US" xlink:label="lab_adam_OTHERINCOMEEXPENSEAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OTHER INCOME (EXPENSE) [Abstract]</link:label>
    <link:label id="lab_adam_OTHERINCOMEEXPENSEAbstract_documentation_en-US" xlink:label="lab_adam_OTHERINCOMEEXPENSEAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OTHER INCOME (EXPENSE)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OTHERINCOMEEXPENSEAbstract" xlink:href="adam-20251231.xsd#adam_OTHERINCOMEEXPENSEAbstract"/>
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    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_e141aee1-0967-4ec8-b28e-c985df079d0c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherAssetsMiscellaneous_label_en-US" xlink:label="lab_us-gaap_OtherAssetsMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsMiscellaneous" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsMiscellaneous"/>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_019b9207-423f-7e29-96c4-d70559d70523_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_adam_NYMPreferredTrustIIMember_e613fdf2-165c-4a2a-b7c6-50cdf1fddf9a_terseLabel_en-US" xlink:label="lab_adam_NYMPreferredTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust II</link:label>
    <link:label id="lab_adam_NYMPreferredTrustIIMember_label_en-US" xlink:label="lab_adam_NYMPreferredTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust II [Member]</link:label>
    <link:label id="lab_adam_NYMPreferredTrustIIMember_documentation_en-US" xlink:label="lab_adam_NYMPreferredTrustIIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust II.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NYMPreferredTrustIIMember" xlink:href="adam-20251231.xsd#adam_NYMPreferredTrustIIMember"/>
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    <link:label id="lab_us-gaap_SeriesDPreferredStockMember_4d1668c9-ed24-4cfd-aef0-a5d15adb6dd2_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesDPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series D Preferred Stock</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesDPreferredStockMember" xlink:to="lab_us-gaap_SeriesDPreferredStockMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
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    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_3d4771fe-9619-4f2f-87b6-189695bf1786_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Collateralized Debt Obligation Securities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_e5e00b96-a35f-4dbc-8205-dbb4868642a3_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-term Debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock"/>
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    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
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    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_747bd72b-dbfa-4405-b1de-830f00d26f51_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
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    <link:label id="lab_adam_NonCashInvestmentActivitiesAbstract_079ee284-acd0-4bed-ac74-e7adfd0774ed_terseLabel_en-US" xlink:label="lab_adam_NonCashInvestmentActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Cash Investing Activities:</link:label>
    <link:label id="lab_adam_NonCashInvestmentActivitiesAbstract_label_en-US" xlink:label="lab_adam_NonCashInvestmentActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Cash Investment Activities:</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NonCashInvestmentActivitiesAbstract" xlink:href="adam-20251231.xsd#adam_NonCashInvestmentActivitiesAbstract"/>
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    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_019c222d-e4be-7c13-ab00-d0f4e1165edd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Originations of residential loans held for sale</link:label>
    <link:label id="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Origination, Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForOriginationOfMortgageLoansHeldForSale"/>
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    <link:label id="lab_adam_DebtIssuanceCostsAmortizationRate_21e1ad45-e160-43bb-8fbe-79b79d66c343_terseLabel_en-US" xlink:label="lab_adam_DebtIssuanceCostsAmortizationRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs, amortization rate</link:label>
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    <link:label id="lab_adam_DebtIssuanceCostsAmortizationRate_documentation_en-US" xlink:label="lab_adam_DebtIssuanceCostsAmortizationRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Amortization Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtIssuanceCostsAmortizationRate" xlink:href="adam-20251231.xsd#adam_DebtIssuanceCostsAmortizationRate"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_e873cee6-f31d-4bda-b880-c2da071d34f4_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_f5ded42c-a81b-43e8-8902-90650ca18b5d_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at the end of period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
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    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019bf8a6-7dd6-7a80-8472-7a69ed6ced98_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
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    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain_04311e50-23a9-4d6f-b708-ae2e9455470b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseTypeDomain"/>
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    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_68d9da91-e8ee-459e-a658-4476026d1cfa_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock"/>
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    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_fef4d616-6636-4d04-9fd0-612be13ec292_verboseLabel_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Balance Sheet Reported Amounts of Mortgage Loans on Real Estate</link:label>
    <link:label id="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward_label_en-US" xlink:label="lab_us-gaap_MovementInMortgageLoansOnRealEstateRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Movement in Mortgage Loans on Real Estate [Roll Forward]</link:label>
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    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
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    <link:label id="lab_dei_EntityFilerCategory_1c77f380-4488-4186-a182-2992ba3c8f6a_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_e33475fa-5fce-4c0f-ae0a-6bcef019c18f_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_4f5891ad-80cd-463b-a6eb-143811be4210_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Benefit at statutory rate (as a percent)</link:label>
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    <link:label id="lab_adam_HudsonBridgeAptsLLCSeriesABriarHillAptsLLCKingsGlenAptssLLCFlagstoneAptsLLCBrookfieldAptsIILLCSeriesBAndSilberJBSMPropertiesLLCCollectivelyMember_e0799857-3ce8-4532-b92a-4a88f4383c5d_terseLabel_en-US" xlink:label="lab_adam_HudsonBridgeAptsLLCSeriesABriarHillAptsLLCKingsGlenAptssLLCFlagstoneAptsLLCBrookfieldAptsIILLCSeriesBAndSilberJBSMPropertiesLLCCollectivelyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hudson Bridge Apartments, LLC - Series A, Briar Hill Apartments, LLC, Kings Glen Apartments, LLC, Flagstone Apartments, LLC, Brookfield Apartments II, LLC - Series B, and Silber JBSM Properties, LLC (collectively)</link:label>
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    <link:label id="lab_adam_FinancialInstrumentInterestTypeAxis_019b0754-a148-7fcf-a431-94abbda6fd38_terseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentInterestTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument Interest Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019bf84d-4f6a-73c7-9a7f-ed819cbd64b5_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
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    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_82c7e2c7-db90-4352-9926-0d031f5a7ba3_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationAxis_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationAxis" xlink:to="lab_us-gaap_BalanceSheetLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization_6a087f30-5a7e-400a-b27e-dca7f8cd4b22_totalLabel_en-US" xlink:label="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income before debt service and depreciation and amortization</link:label>
    <link:label id="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization_label_en-US" xlink:label="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Before Debt Service And Depreciation And Amortization</link:label>
    <link:label id="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization_documentation_en-US" xlink:label="lab_adam_IncomeBeforeDebtServiceAndDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income Before Debt Service And Depreciation And Amortization</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_a91b5bfa-f8ba-45c5-9487-1cce3388a0cf_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
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    <link:label id="lab_adam_PreferredEquityInvestmentonMultifamilyPropertiesMember_a64c9cab-d814-4612-b289-df4b4c9b747b_terseLabel_en-US" xlink:label="lab_adam_PreferredEquityInvestmentonMultifamilyPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred equity investments in multi-family properties</link:label>
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    <link:label id="lab_adam_PreferredEquityInvestmentonMultifamilyPropertiesMember_documentation_en-US" xlink:label="lab_adam_PreferredEquityInvestmentonMultifamilyPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Equity Investment on Multi-family Properties [Member]</link:label>
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    <link:label id="lab_adam_NumberOfRealEstatePropertiesHeldForSale_4958f4d9-c3a9-4fc8-b77a-7ffe89443455_terseLabel_en-US" xlink:label="lab_adam_NumberOfRealEstatePropertiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of properties held for sale</link:label>
    <link:label id="lab_adam_NumberOfRealEstatePropertiesHeldForSale_label_en-US" xlink:label="lab_adam_NumberOfRealEstatePropertiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Real Estate Properties Held For Sale</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_5b7a1cd1-e5f5-43ad-a359-4b999c944cbc_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition Date Fair Value</link:label>
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    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
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    <link:label id="lab_adam_NoncashOrPartNoncashAcquisitionDistributionOfMortgageServicingRights_3b74869a-2d02-4bd0-9f67-dc3aff2e3b91_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashAcquisitionDistributionOfMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distribution of mortgage servicing rights from equity investment</link:label>
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    <link:label id="lab_dei_EntityAddressAddressLine1_19fdb68d-827f-4212-8175-8af1c8e2ebc4_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateForeclosures_3da836b4-8b4e-44a3-afae-faea5e004e46_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateForeclosures" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer to REO</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateForeclosures_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateForeclosures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateForeclosures" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstateForeclosures"/>
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    <link:label id="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption_5686beed-ac85-48f7-9d18-bf8fd0d98b2f_terseLabel_en-US" xlink:label="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, interest rate increase, non-redemption</link:label>
    <link:label id="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption_label_en-US" xlink:label="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Increase, Non-Redemption</link:label>
    <link:label id="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption_documentation_en-US" xlink:label="lab_adam_DebtInstrumentInterestRateIncreaseNonRedemption" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate Increase, Non-Redemption</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtInstrumentInterestRateIncreaseNonRedemption" xlink:href="adam-20251231.xsd#adam_DebtInstrumentInterestRateIncreaseNonRedemption"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_74fc7c45-c53d-452a-971b-515946c2e86e_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability_1e87edea-bf01-43b5-be89-ce6c821bfe8a_verboseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability_b9581c33-9da4-4e95-bed2-73abd1e33748_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements, maturities</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Repurchase Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseRepurchaseLiability"/>
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    <link:label id="lab_adam_TenorSpreadAdjustmentMember_019c4161-c79e-7620-b1ac-c4db3ec55ec4_terseLabel_en-US" xlink:label="lab_adam_TenorSpreadAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tenor Spread Adjustment</link:label>
    <link:label id="lab_adam_TenorSpreadAdjustmentMember_label_en-US" xlink:label="lab_adam_TenorSpreadAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tenor Spread Adjustment [Member]</link:label>
    <link:label id="lab_adam_TenorSpreadAdjustmentMember_documentation_en-US" xlink:label="lab_adam_TenorSpreadAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tenor Spread Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_TenorSpreadAdjustmentMember" xlink:href="adam-20251231.xsd#adam_TenorSpreadAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_TenorSpreadAdjustmentMember" xlink:to="lab_adam_TenorSpreadAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_9adca5e6-40cf-421a-869f-9c394bc88cc0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_419e468a-a0a7-4bef-af79-d9db46c2c397_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_f5a019a0-0588-458c-9af7-b5b9844b5d58_periodStartLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_04c48276-dde6-4ac7-b144-54e797dafd3a_periodEndLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount_label_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest, Equity, Carrying Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:to="lab_us-gaap_RedeemableNoncontrollingInterestEquityCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_HoustonTXMember_2ca9204b-7e23-4c9b-84cc-e39656845fb5_terseLabel_en-US" xlink:label="lab_adam_HoustonTXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Houston, TX</link:label>
    <link:label id="lab_adam_HoustonTXMember_label_en-US" xlink:label="lab_adam_HoustonTXMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Houston, TX [Member]</link:label>
    <link:label id="lab_adam_HoustonTXMember_documentation_en-US" xlink:label="lab_adam_HoustonTXMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Houston, TX</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_HoustonTXMember" xlink:href="adam-20251231.xsd#adam_HoustonTXMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_HoustonTXMember" xlink:to="lab_adam_HoustonTXMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_60bff050-fc0d-472f-81ef-c0ebd3b2fc2d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Investment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Real Estate Properties [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRealEstatePropertiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
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    <link:label id="lab_adam_FannieMaeMember_5a8a8b35-3935-4a5b-a712-650f66bff59a_terseLabel_en-US" xlink:label="lab_adam_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:label id="lab_adam_FannieMaeMember_label_en-US" xlink:label="lab_adam_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fannie Mae [Member]</link:label>
    <link:label id="lab_adam_FannieMaeMember_documentation_en-US" xlink:label="lab_adam_FannieMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fannie Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FannieMaeMember" xlink:href="adam-20251231.xsd#adam_FannieMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FannieMaeMember" xlink:to="lab_adam_FannieMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuritiesInvestmentMember_0588a382-326d-48aa-acbb-df9cc20b6212_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities</link:label>
    <link:label id="lab_us-gaap_SecuritiesInvestmentMember_label_en-US" xlink:label="lab_us-gaap_SecuritiesInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities Investment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuritiesInvestmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuritiesInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesInvestmentMember" xlink:to="lab_us-gaap_SecuritiesInvestmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019be5a9-d5f8-7850-ba40-d61511559ede_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_db5fd9e2-803f-4654-8f32-28591d17fd7c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
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    <link:label id="lab_adam_UnrealizedGainLossLoans_documentation_en-US" xlink:label="lab_adam_UnrealizedGainLossLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) Loans</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesMember_bfb89387-b2dd-4b21-a350-de4e65185d93_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwards"/>
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    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseCarryingAmounts_019b143e-97f9-70a0-9b9d-aa16a3d4e583_netLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseCarryingAmounts" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements and warehouse facilities</link:label>
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    <link:label id="lab_adam_DallasTXMember_cf84fa3d-04f2-4718-9db4-948387c0001b_terseLabel_en-US" xlink:label="lab_adam_DallasTXMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dallas, TX</link:label>
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    <link:label id="lab_us-gaap_LaborAndRelatedExpense_539276dd-97dd-47f3-8007-0b1dc7351b44_terseLabel_en-US" xlink:label="lab_us-gaap_LaborAndRelatedExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Salaries and benefits expense</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LaborAndRelatedExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LaborAndRelatedExpense"/>
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    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_5006ca2a-cc17-4132-a677-e2c5ba422601_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Senior Unsecured Notes</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireInvestments_554501f4-f1e1-4bca-9926-f68dba73cedf_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases and originations of residential loans</link:label>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_e37c04a6-a22b-439e-b03e-f37ba43e21ac_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
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    <link:label id="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock_9e57e7e6-ed77-43d6-a86c-8c773b54449a_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Loans and Residential Loans Held for Sale, at Fair Value</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans at Fair Value [Text Block]</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansAtFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:to="lab_adam_ResidentialMortgageLoansAtFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_019c2f80-0000-77b7-bda6-b18bfecfe1dc_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_f34d2d72-5890-44e8-8122-a1e9432b1ab2_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate, estimated fair value</link:label>
    <link:label id="lab_us-gaap_LongTermDebtFairValue_label_en-US" xlink:label="lab_us-gaap_LongTermDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtFairValue" xlink:to="lab_us-gaap_LongTermDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_66931352-54db-4602-b20b-8fe655a1b5f1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Measurement Inputs and Valuation Techniques</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock"/>
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    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
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    <link:label id="lab_us-gaap_SecondMortgageMember_61f6b5cd-2c2b-49a2-bedd-5d9fe5bcfe91_terseLabel_en-US" xlink:label="lab_us-gaap_SecondMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Second lien loans</link:label>
    <link:label id="lab_us-gaap_SecondMortgageMember_label_en-US" xlink:label="lab_us-gaap_SecondMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Second Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecondMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecondMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecondMortgageMember" xlink:to="lab_us-gaap_SecondMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_47e49d37-cf01-4f9d-a7c2-2207fd53f91b_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_bc93629f-97af-4e6c-8fc5-1c1fbd1321dd_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
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    <link:label id="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable_2ca42729-0d4a-4d89-a992-ca21f6364179_terseLabel_en-US" xlink:label="lab_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Values Derivatives, Balance Sheet Location, by Derivative Contract Type [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValuesDerivativesBalanceSheetLocationByDerivativeContractTypeByHedgingDesignationTable"/>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_e20fc23d-bb91-4fe3-80cf-ed71424f804f_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reverse stock split (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1"/>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
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    <link:label id="lab_us-gaap_NotDesignatedAsHedgingInstrumentTradingMember_758d847b-1580-461a-8e71-711e326b24f2_terseLabel_en-US" xlink:label="lab_us-gaap_NotDesignatedAsHedgingInstrumentTradingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading</link:label>
    <link:label id="lab_us-gaap_NotDesignatedAsHedgingInstrumentTradingMember_label_en-US" xlink:label="lab_us-gaap_NotDesignatedAsHedgingInstrumentTradingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Not Designated as Hedging Instrument, Trading [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotDesignatedAsHedgingInstrumentTradingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotDesignatedAsHedgingInstrumentTradingMember"/>
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    <link:label id="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans_532d0d7f-198a-49b2-b379-8f8079dad5cc_terseLabel_en-US" xlink:label="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unpaid Principal Balance</link:label>
    <link:label id="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans_label_en-US" xlink:label="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity And Mezzanine Loans, Principal Amount Of Delinquent Loans</link:label>
    <link:label id="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans_documentation_en-US" xlink:label="lab_adam_EquityAndMezzanineLoansPrincipalAmountOfDelinquentLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity And Mezzanine Loans, Principal Amount Of Delinquent Loans</link:label>
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    <link:label id="lab_us-gaap_InvestmentTypeAxis_a3585f65-080b-4b21-81d3-40369180ca6e_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
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    <link:label id="lab_us-gaap_Investments_33fb18a1-1fd7-49f0-a000-f7f8fcd2e218_terseLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
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    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019bf84d-4f6a-7ca6-ae75-71ed44a8eec8_verboseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
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    <link:label id="lab_adam_NotionalAmountOfOtherDerivativeAdditionsTransfersIn_ed2e9a8c-e40d-48b1-8257-88fdacd739e5_terseLabel_en-US" xlink:label="lab_adam_NotionalAmountOfOtherDerivativeAdditionsTransfersIn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions/Transfers In</link:label>
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    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateTransfersIn_019c41ea-6558-7f6e-a8cd-8f3cc4b11f90_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateTransfersIn" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers in</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateTransfersIn" xlink:href="adam-20251231.xsd#adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateTransfersIn"/>
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    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseAxis_1e2a7508-7a2e-4a2a-9955-18980c353d17_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Securities or Other Assets Sold under Agreements to Repurchase [Axis]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseAxis_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Securities or Other Assets Sold under Agreements to Repurchase [Axis]</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeOther_042e304d-6c9e-434a-acff-8c9ea4cec9a5_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_InterestIncomeOther_label_en-US" xlink:label="lab_us-gaap_InterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Income, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestIncomeOther" xlink:to="lab_us-gaap_InterestIncomeOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_20cb1c6a-5b6a-462c-9ca3-6bb84eedf728_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, dividend rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
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    <link:label id="lab_us-gaap_NoncontrollingInterestInVariableInterestEntity_1ffff224-1cc0-47dd-95d7-465783509308_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestInVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interest in VIE</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestInVariableInterestEntity_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestInVariableInterestEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest in Variable Interest Entity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestInVariableInterestEntity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestInVariableInterestEntity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestInVariableInterestEntity" xlink:to="lab_us-gaap_NoncontrollingInterestInVariableInterestEntity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium_eb2d1cb1-eb75-40fa-9b38-b712bac52c5b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amortization of premium</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Amortization of Premium</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstateAmortizationOfPremium"/>
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    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_248d998a-a301-4f31-94a6-570285dd57f5_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageServicingRightsMember_444e7763-679c-4478-b752-4d590b24d7ac_terseLabel_en-US" xlink:label="lab_adam_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MSRs</link:label>
    <link:label id="lab_adam_MortgageServicingRightsMember_label_en-US" xlink:label="lab_adam_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights [Member]</link:label>
    <link:label id="lab_adam_MortgageServicingRightsMember_documentation_en-US" xlink:label="lab_adam_MortgageServicingRightsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageServicingRightsMember" xlink:href="adam-20251231.xsd#adam_MortgageServicingRightsMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_b148557a-de6c-45ee-a0d8-d3bb5817cc38_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_c7353cb4-35b7-4ca8-8134-5e15d1032a8a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Company's Repurchase Agreements</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRepurchaseAgreements_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Repurchase Agreements [Table Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRepurchaseAgreements" xlink:to="lab_us-gaap_ScheduleOfRepurchaseAgreements" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour_dd3c849f-21bf-407e-8bc6-c56f079d93cd_terseLabel_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour_label_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year Four</link:label>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour_documentation_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year Four</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_4920eaca-8bfb-4c26-9f40-19ad71663c33_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_bf3c0028-ce5d-4145-bfa5-a0255ff6095a_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
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    <link:label id="lab_us-gaap_VariableInterestEntityMeasureOfActivityAbstract_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityMeasureOfActivityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Measure of Activity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_MinorityInterest_eb91420b-572f-4a92-b7c8-0072e2ea6e47_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_d9481f09-15f6-4525-b4f6-976acb1d34a3_verboseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeconsolidationGainOrLossAmount_ebd6b4c0-1526-49e4-8c9e-c1ec90f45292_terseLabel_en-US" xlink:label="lab_us-gaap_DeconsolidationGainOrLossAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total gain on de-consolidation of Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_DeconsolidationGainOrLossAmount_label_en-US" xlink:label="lab_us-gaap_DeconsolidationGainOrLossAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deconsolidation, Gain (Loss), Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeconsolidationGainOrLossAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeconsolidationGainOrLossAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeconsolidationGainOrLossAmount" xlink:to="lab_us-gaap_DeconsolidationGainOrLossAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019c221f-fa7e-7c65-b038-e7f963e5c293_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other gains, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax_37e22b09-db33-401e-8ec3-9bf7021f15d3_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pretax loss of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Individually Significant Component Disposed of or Held-for-Sale, Excluding Discontinued Operations, before Income Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax" xlink:to="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsBeforeIncomeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UnsecuredDebtFairValueDisclosure_8c981888-d849-401f-8345-010ecccd3538_verboseLabel_en-US" xlink:label="lab_adam_UnsecuredDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes</link:label>
    <link:label id="lab_adam_UnsecuredDebtFairValueDisclosure_label_en-US" xlink:label="lab_adam_UnsecuredDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Fair Value Disclosure</link:label>
    <link:label id="lab_adam_UnsecuredDebtFairValueDisclosure_documentation_en-US" xlink:label="lab_adam_UnsecuredDebtFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unsecured Debt, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnsecuredDebtFairValueDisclosure" xlink:href="adam-20251231.xsd#adam_UnsecuredDebtFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnsecuredDebtFairValueDisclosure" xlink:to="lab_adam_UnsecuredDebtFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_InterestRateStepUpDomain_8ad68786-592e-4bb8-a58f-7320d803b2a4_terseLabel_en-US" xlink:label="lab_adam_InterestRateStepUpDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Domain]</link:label>
    <link:label id="lab_adam_InterestRateStepUpDomain_label_en-US" xlink:label="lab_adam_InterestRateStepUpDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Domain]</link:label>
    <link:label id="lab_adam_InterestRateStepUpDomain_documentation_en-US" xlink:label="lab_adam_InterestRateStepUpDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_InterestRateStepUpDomain" xlink:href="adam-20251231.xsd#adam_InterestRateStepUpDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_InterestRateStepUpDomain" xlink:to="lab_adam_InterestRateStepUpDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_52b098ad-8e7a-4994-8ce9-5dccf2ff1a0b_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax (benefit) provision</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable_c14bd7ca-820d-4e3b-aab8-e32aed061af3_terseLabel_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable_label_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty, Accrued Interest Payable</link:label>
    <link:label id="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable_documentation_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty, Accrued Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:href="adam-20251231.xsd#adam_RepurchaseAgreementCounterpartyAccruedInterestPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:to="lab_adam_RepurchaseAgreementCounterpartyAccruedInterestPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ConstructiveLoansLLCMember_cf4d3d33-6e28-4260-a601-4433195bdee4_terseLabel_en-US" xlink:label="lab_adam_ConstructiveLoansLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constructive Loans LLC</link:label>
    <link:label id="lab_adam_ConstructiveLoansLLCMember_label_en-US" xlink:label="lab_adam_ConstructiveLoansLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Constructive Loans LLC [Member]</link:label>
    <link:label id="lab_adam_ConstructiveLoansLLCMember_documentation_en-US" xlink:label="lab_adam_ConstructiveLoansLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Constructive Loans LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ConstructiveLoansLLCMember" xlink:href="adam-20251231.xsd#adam_ConstructiveLoansLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ConstructiveLoansLLCMember" xlink:to="lab_adam_ConstructiveLoansLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_d2e771d2-172e-4990-a884-225a3394eaf5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_d1b533b9-cbc1-4fff-a220-773b48456673_verboseLabel_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Net</link:label>
    <link:label id="lab_us-gaap_RealEstateDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateDisclosureTextBlock" xlink:to="lab_us-gaap_RealEstateDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_HoldbackForRepresentationsAndWarranties_019c27fb-01ae-7453-9fa0-cf182d67ebe2_terseLabel_en-US" xlink:label="lab_adam_HoldbackForRepresentationsAndWarranties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Holdback for representations and warranties</link:label>
    <link:label id="lab_adam_HoldbackForRepresentationsAndWarranties_label_en-US" xlink:label="lab_adam_HoldbackForRepresentationsAndWarranties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Holdback For Representations And Warranties</link:label>
    <link:label id="lab_adam_HoldbackForRepresentationsAndWarranties_documentation_en-US" xlink:label="lab_adam_HoldbackForRepresentationsAndWarranties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Holdback For Representations And Warranties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_HoldbackForRepresentationsAndWarranties" xlink:href="adam-20251231.xsd#adam_HoldbackForRepresentationsAndWarranties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_HoldbackForRepresentationsAndWarranties" xlink:to="lab_adam_HoldbackForRepresentationsAndWarranties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax_a0e46966-c3c1-4ce3-8aab-2d946296213c_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Pretax loss of disposal group attributable to Company's common stockholders</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Individually Significant Component Disposed of or Held-for-Sale, Excluding Discontinued Operations, Attributable to Parent, before Income Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax" xlink:to="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToParentBeforeIncomeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale_77bad5ee-08b0-40d2-a1dd-c49255f08a41_negatedTerseLabel_en-US" xlink:label="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cash reclassified from assets of disposal group held for sale</link:label>
    <link:label id="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale_label_en-US" xlink:label="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Reclassified To Assets Of Disposal Group Held For Sale</link:label>
    <link:label id="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale_documentation_en-US" xlink:label="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash Reclassified To Assets Of Disposal Group Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:href="adam-20251231.xsd#adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:to="lab_adam_CashReclassifiedToAssetsOfDisposalGroupHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral_27591baa-3a5c-4bad-98da-72d5c94271a3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral_c66ca756-fcdb-4d91-b2ab-31bae18b285e_totalLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Amounts of Assets (Liabilities) Presented in Balance Sheets</link:label>
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    <link:label id="lab_adam_DeferredStockUnitsMember_label_en-US" xlink:label="lab_adam_DeferredStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Stock Units [Member]</link:label>
    <link:label id="lab_adam_DeferredStockUnitsMember_documentation_en-US" xlink:label="lab_adam_DeferredStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DeferredStockUnitsMember" xlink:href="adam-20251231.xsd#adam_DeferredStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DeferredStockUnitsMember" xlink:to="lab_adam_DeferredStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NoncashOrPartNoncashAcquisitionConsolidationOfMortgagesPayableOnRealEstateHeld_b59c57c7-39f1-487b-bd78-293d36ebf8fd_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashAcquisitionConsolidationOfMortgagesPayableOnRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation of mortgages payable on real estate held in Consolidated VIEs</link:label>
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    <link:label id="lab_adam_SeniorUnsecuredNotesMember_3c4185dd-c454-4e0c-9e02-2d6d49ab49eb_terseLabel_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes at amortized cost, net</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesMember_cb203b41-b8cd-4ae5-8590-1783b1619895_verboseLabel_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes at amortized cost, net</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesMember_label_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes [Member]</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesMember_documentation_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SeniorUnsecuredNotesMember" xlink:href="adam-20251231.xsd#adam_SeniorUnsecuredNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SeniorUnsecuredNotesMember" xlink:to="lab_adam_SeniorUnsecuredNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SwapMaturities2030Member_019c2c36-7c14-78f3-8894-0453f119d628_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_adam_SwapMaturities2030Member_label_en-US" xlink:label="lab_adam_SwapMaturities2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swap Maturities 2030 [Member]</link:label>
    <link:label id="lab_adam_SwapMaturities2030Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2030Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2030Member"/>
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    <link:label id="lab_adam_ConstructiveSegmentMember_019bf8a6-7dd6-743c-98ac-974887825ab9_terseLabel_en-US" xlink:label="lab_adam_ConstructiveSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Constructive</link:label>
    <link:label id="lab_adam_ConstructiveSegmentMember_label_en-US" xlink:label="lab_adam_ConstructiveSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Constructive Segment [Member]</link:label>
    <link:label id="lab_adam_ConstructiveSegmentMember_documentation_en-US" xlink:label="lab_adam_ConstructiveSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Constructive Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ConstructiveSegmentMember" xlink:href="adam-20251231.xsd#adam_ConstructiveSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ConstructiveSegmentMember" xlink:to="lab_adam_ConstructiveSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableSignificantPurchases_9cc6b44a-b4b3-431a-a054-a0320def91e6_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableSignificantPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase of residential loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableSignificantPurchases_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableSignificantPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Purchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableSignificantPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableSignificantPurchases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableSignificantPurchases" xlink:to="lab_us-gaap_FinancingReceivableSignificantPurchases" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_OtherLiabilitiesMiscellaneous_6b250e56-10ee-482d-88de-888b61da7c7c_terseLabel_en-US" xlink:label="lab_adam_OtherLiabilitiesMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_adam_OtherLiabilitiesMiscellaneous_label_en-US" xlink:label="lab_adam_OtherLiabilitiesMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Miscellaneous</link:label>
    <link:label id="lab_adam_OtherLiabilitiesMiscellaneous_documentation_en-US" xlink:label="lab_adam_OtherLiabilitiesMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Liabilities, Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OtherLiabilitiesMiscellaneous" xlink:href="adam-20251231.xsd#adam_OtherLiabilitiesMiscellaneous"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_OtherLiabilitiesMiscellaneous" xlink:to="lab_adam_OtherLiabilitiesMiscellaneous" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_dbcfece8-2ae3-47ee-8fbf-4a81efc4fe02_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_label_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentsIncorporatedByReferenceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:to="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances_0c6cfc08-353b-42a8-a41c-8e3c80333a08_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Encumbrances</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation, Amount of Encumbrances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationAmountOfEncumbrances"/>
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    <link:label id="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock_ddb8677a-8d40-4696-8678-ffa6f6a58c53_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Borrowings Under Purchase Agreements Secured by Investments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock"/>
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    <link:label id="lab_us-gaap_MeasurementInputAppraisedValueMember_96922903-b3df-4f03-a643-91c84c221c5d_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputAppraisedValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property value</link:label>
    <link:label id="lab_us-gaap_MeasurementInputAppraisedValueMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputAppraisedValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Appraised Value [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputAppraisedValueMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputAppraisedValueMember"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_5b3290b7-7521-452b-918a-92b4552991b1_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentLineItems_21430cf8-b8f6-4249-863e-4754202ff58a_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment [Line Items]</link:label>
    <link:label id="lab_us-gaap_LongTermPurchaseCommitmentLineItems_label_en-US" xlink:label="lab_us-gaap_LongTermPurchaseCommitmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Purchase Commitment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermPurchaseCommitmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermPurchaseCommitmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermPurchaseCommitmentLineItems" xlink:to="lab_us-gaap_LongTermPurchaseCommitmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_6645edf3-796d-4cb5-95fb-0da0bda7540d_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_e9bbdfe4-e42a-48d4-a4b9-cbfc393cf1c4_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_0082554c-0a49-46fe-b9a1-e4d10dce144f_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_a3173b8c-56c9-45f9-a487-eb18a8f0e743_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_34b45646-5dd4-4e1c-904d-c9181bb46f1c_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_us-gaap_PerformanceSharesMember_525f11e9-615c-4205-9371-ee1d01169d80_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Shares</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_af60f3fb-066b-4714-87c2-78b228bff8c8_verboseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">PSUs</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_label_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Shares [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PerformanceSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PerformanceSharesMember" xlink:to="lab_us-gaap_PerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtPnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtPnsnAdjsSvcCstMember" xlink:to="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NoninterestIncomeExpenseOther_5e6787d4-adbe-440f-b262-1b4653f208b7_terseLabel_en-US" xlink:label="lab_adam_NoninterestIncomeExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_adam_NoninterestIncomeExpenseOther_7f751887-a3b0-4c65-b4b1-0b35c72196c8_verboseLabel_en-US" xlink:label="lab_adam_NoninterestIncomeExpenseOther" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_adam_NoninterestIncomeExpenseOther_label_en-US" xlink:label="lab_adam_NoninterestIncomeExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income (Expense), Other</link:label>
    <link:label id="lab_adam_NoninterestIncomeExpenseOther_documentation_en-US" xlink:label="lab_adam_NoninterestIncomeExpenseOther" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noninterest Income (Expense), Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NoninterestIncomeExpenseOther" xlink:href="adam-20251231.xsd#adam_NoninterestIncomeExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NoninterestIncomeExpenseOther" xlink:to="lab_adam_NoninterestIncomeExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ValuationTechniqueTransactionPriceMember_019c2856-fbcf-7fef-b38c-e951fcccb6d9_terseLabel_en-US" xlink:label="lab_adam_ValuationTechniqueTransactionPriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction price</link:label>
    <link:label id="lab_adam_ValuationTechniqueTransactionPriceMember_label_en-US" xlink:label="lab_adam_ValuationTechniqueTransactionPriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Transaction Price [Member]</link:label>
    <link:label id="lab_adam_ValuationTechniqueTransactionPriceMember_documentation_en-US" xlink:label="lab_adam_ValuationTechniqueTransactionPriceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Transaction Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ValuationTechniqueTransactionPriceMember" xlink:href="adam-20251231.xsd#adam_ValuationTechniqueTransactionPriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ValuationTechniqueTransactionPriceMember" xlink:to="lab_adam_ValuationTechniqueTransactionPriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust_1fb894a9-6694-43cb-a251-ad1c5753c842_negatedTerseLabel_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers to securitization trust, net</link:label>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust_label_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers Out Of Level 3 To Securitization Trust</link:label>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust_documentation_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers Out Of Level 3 To Securitization Trust</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:href="adam-20251231.xsd#adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:to="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3ToSecuritizationTrust" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_38fb0b6d-ad13-48d3-a7b6-bb427df25b69_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_f8bc5c52-23ca-42ee-b806-6683c42592d3_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecurityDeposit_8a192a51-68d8-4968-bfe0-16b4a0cb61ad_terseLabel_en-US" xlink:label="lab_us-gaap_SecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security deposit</link:label>
    <link:label id="lab_us-gaap_SecurityDeposit_label_en-US" xlink:label="lab_us-gaap_SecurityDeposit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Deposit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecurityDeposit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecurityDeposit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecurityDeposit" xlink:to="lab_us-gaap_SecurityDeposit" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets_25353a51-d656-4613-8b6a-e7396c43b8ab_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets in disposal group held for sale, carrying value</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets_label_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operations, Derivative Assets</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets_documentation_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operations, Derivative Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationsDerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets_383b720f-e6bf-4e32-9a32-ecf544e0cf97_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_3a2435e8-5322-42e7-9f46-5ffec59da535_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems_label_en-US" xlink:label="lab_us-gaap_AccountsNotesAndLoansReceivableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts, Notes, Loans and Financing Receivable [Line Items]</link:label>
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    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_019bf84d-4f6a-712d-9c91-61b7680a7707_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Company's common stockholders</link:label>
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    <link:label id="lab_adam_A2017PlanMember_93e1c112-2ffb-49a8-bd4b-e6eb2ce049d7_terseLabel_en-US" xlink:label="lab_adam_A2017PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2017 Plan</link:label>
    <link:label id="lab_adam_A2017PlanMember_label_en-US" xlink:label="lab_adam_A2017PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2017 Plan [Member]</link:label>
    <link:label id="lab_adam_A2017PlanMember_documentation_en-US" xlink:label="lab_adam_A2017PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2017 Plan [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A2017PlanMember" xlink:href="adam-20251231.xsd#adam_A2017PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_A2017PlanMember" xlink:to="lab_adam_A2017PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_97efde28-95f2-456d-b701-eb363880105b_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Debt</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
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    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
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    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_84e6226e-7fa7-470b-9dee-07bccbfcfd0f_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends and dividend equivalents payable</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_f49b4848-dccd-4791-abc7-71626d33af9c_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET INCOME (LOSS) ATTRIBUTABLE TO COMPANY'S COMMON STOCKHOLDERS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_604dc2ef-614d-481d-9f1a-77ea83e420f1_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stockholders' Equity Note [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteAbstract"/>
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    <link:label id="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable_392a5c34-7f6c-4da6-86f5-1ff38edf54f1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAssetsSoldUnderAgreementsToRepurchaseTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Sold under Agreement to Repurchase</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_33fcf197-c512-4b3c-bbc5-442b2c72bbc6_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
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    <link:label id="lab_adam_MezzanineLoanandPreferredEquityInvestmentsMember_55389495-6d9f-473f-9ba2-3113f43957c2_terseLabel_en-US" xlink:label="lab_adam_MezzanineLoanandPreferredEquityInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family Loans</link:label>
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    <link:label id="lab_adam_MezzanineLoanandPreferredEquityInvestmentsMember_documentation_en-US" xlink:label="lab_adam_MezzanineLoanandPreferredEquityInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mezzanine Loan and Preferred Equity Investments [Member]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_c6e0cff6-6fc3-4d1f-82f3-1286f4dc97e8_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixturesAndEquipmentGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixturesAndEquipmentGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixturesAndEquipmentGross" xlink:to="lab_us-gaap_FixturesAndEquipmentGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_21c3c815-c683-470e-80ab-a53c94f2ed5f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan_019c222d-1327-7816-829a-36292d6216a5_negatedTerseLabel_en-US" xlink:label="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income from preferred equity, mezzanine loan and equity investments</link:label>
    <link:label id="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan_label_en-US" xlink:label="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) From Equity Method Investments, Preferred Equity and Mezzanine Loan</link:label>
    <link:label id="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan_documentation_en-US" xlink:label="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Income (Loss) From Equity Method Investments, Preferred Equity and Mezzanine Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:href="adam-20251231.xsd#adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:to="lab_adam_IncomeLossFromEquityMethodInvestmentsPreferredEquityAndMezzanineLoan" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageBankingActivitiesNet_019b8cc3-4b01-7239-b659-9b7dd048fa9e_terseLabel_en-US" xlink:label="lab_adam_MortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage banking activities, net</link:label>
    <link:label id="lab_adam_MortgageBankingActivitiesNet_label_en-US" xlink:label="lab_adam_MortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Banking Activities Net</link:label>
    <link:label id="lab_adam_MortgageBankingActivitiesNet_documentation_en-US" xlink:label="lab_adam_MortgageBankingActivitiesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Banking Activities Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageBankingActivitiesNet" xlink:href="adam-20251231.xsd#adam_MortgageBankingActivitiesNet"/>
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    <link:label id="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember_32855407-de23-49cf-bb5a-ecce1fd0c40a_terseLabel_en-US" xlink:label="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-Family Preferred Equity Ownership Interests</link:label>
    <link:label id="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember_label_en-US" xlink:label="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family Preferred Equity Ownership Interests [Member]</link:label>
    <link:label id="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember_documentation_en-US" xlink:label="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi-Family Preferred Equity Ownership Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:href="adam-20251231.xsd#adam_MultiFamilyPreferredEquityOwnershipInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:to="lab_adam_MultiFamilyPreferredEquityOwnershipInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis_9158c65a-05f4-4b18-a980-fc81fa759538_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Category [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionLoanCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_019bf84d-4f6a-7ce2-9897-9a8479647fee_terseLabel_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_label_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Cash</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash_documentation_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:href="adam-20251231.xsd#adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:to="lab_adam_BusinessCombinationRecognizedAssetAcquiredRestrictedCash" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_9ac649c4-7e0c-49ad-9fd1-7b295a81d8e9_terseLabel_en-US" xlink:label="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">7.000% Series G Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
    <link:label id="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_label_en-US" xlink:label="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">7.000% Series G Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference [Member]</link:label>
    <link:label id="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_documentation_en-US" xlink:label="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">7.000% Series G Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:href="adam-20251231.xsd#adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:to="lab_adam_A7000SeriesGCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures_019c2794-dbcd-7cb4-a0d3-58cf621e7d23_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable to joint venture equity investments in default, number of joint ventures</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures_label_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Mortgages Payable In Default, Number Of Joint Ventures</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures_documentation_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Mortgages Payable In Default, Number Of Joint Ventures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableInDefaultNumberOfJointVentures" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DebtInstrumentPercentageOfPrincipalIssued_2d7ec20f-b8c5-4759-961e-46df11664235_terseLabel_en-US" xlink:label="lab_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, percentage of principal issued</link:label>
    <link:label id="lab_adam_DebtInstrumentPercentageOfPrincipalIssued_label_en-US" xlink:label="lab_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Percentage Of Principal Issued</link:label>
    <link:label id="lab_adam_DebtInstrumentPercentageOfPrincipalIssued_documentation_en-US" xlink:label="lab_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Percentage Of Principal Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:href="adam-20251231.xsd#adam_DebtInstrumentPercentageOfPrincipalIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:to="lab_adam_DebtInstrumentPercentageOfPrincipalIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_f5b9f413-de6b-4230-838f-d9c4a28ba83f_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_a1cc0a1e-bcb3-49cb-8969-64b63b095b31_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_eee4bda9-2b8b-46de-a918-a5418f1aff9e_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_55404e7b-1e0d-48fc-a029-4404b1b7a47d_netLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net investment</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FirstMortgageMember_6cefdca5-f02d-4071-8d2e-6336ffdccb57_terseLabel_en-US" xlink:label="lab_us-gaap_FirstMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">First lien loans</link:label>
    <link:label id="lab_us-gaap_FirstMortgageMember_label_en-US" xlink:label="lab_us-gaap_FirstMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">First Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FirstMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FirstMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FirstMortgageMember" xlink:to="lab_us-gaap_FirstMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_a77bca9d-a500-4188-8241-2223525dd0cb_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Average cost per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_label_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Acquired, Average Cost Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:to="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_d8511153-f57c-4e96-973d-a7ced1cfd2ec_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_82f59d3b-0eda-4213-b7b1-44aabc0b10e5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure_9c5e5c0f-de1b-4a7a-b8b5-0bcaf245086f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure_f6444354-3e22-48ac-8d79-fd1912d07c26_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Equity investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:to="lab_us-gaap_EquityMethodInvestmentsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_135f6fa4-8f62-4c75-91a6-54add2422937_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (Loss) Per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_9de964f3-2daf-40fc-a21a-da8b68646157_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayable_ed0e1597-c14e-44ee-818e-d061a90526f0_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate, net</link:label>
    <link:label id="lab_us-gaap_NotesPayable_a0d07287-cac7-4fee-8821-a70c00e39a78_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable, net in consolidated variable interest entities</link:label>
    <link:label id="lab_us-gaap_NotesPayable_label_en-US" xlink:label="lab_us-gaap_NotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NotesPayable"/>
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    <link:label id="lab_us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships_26e249ca-00d8-4b1a-9b30-b9cea021a49b_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of real estate</link:label>
    <link:label id="lab_us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships_label_en-US" xlink:label="lab_us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment Losses Related to Real Estate Partnerships</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentLossesRelatedToRealEstatePartnerships"/>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_b7fc855b-5543-47a3-b80f-e4d33f40ea64_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Income [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentIncomeReportedAmountsByCategoryTable"/>
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    <link:label id="lab_adam_FFRMI20MidtownLLCMember_ea153262-a333-48cd-82c4-9f9fe102a97c_terseLabel_en-US" xlink:label="lab_adam_FFRMI20MidtownLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">FF/RMI 20 Midtown, LLC</link:label>
    <link:label id="lab_adam_FFRMI20MidtownLLCMember_label_en-US" xlink:label="lab_adam_FFRMI20MidtownLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">FF RMI 20 Midtown, LLC [Member]</link:label>
    <link:label id="lab_adam_FFRMI20MidtownLLCMember_documentation_en-US" xlink:label="lab_adam_FFRMI20MidtownLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">FF RMI 20 Midtown, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FFRMI20MidtownLLCMember" xlink:href="adam-20251231.xsd#adam_FFRMI20MidtownLLCMember"/>
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    <link:label id="lab_srt_RangeAxis_04b29769-e2d3-45ed-afeb-68a659205037_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_ca00434f-efe6-4283-be8d-32bf8767d3ce_terseLabel_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock repurchase program, authorized amount</link:label>
    <link:label id="lab_srt_StockRepurchaseProgramAuthorizedAmount1_label_en-US" xlink:label="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StockRepurchaseProgramAuthorizedAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:to="lab_srt_StockRepurchaseProgramAuthorizedAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU_ea7a7016-203f-434f-98c8-bd3682889aa3_terseLabel_en-US" xlink:label="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of shares per vested RSU (in shares)</link:label>
    <link:label id="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU_label_en-US" xlink:label="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Per RSU</link:label>
    <link:label id="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU_documentation_en-US" xlink:label="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Number Of Shares Per Vested RSU</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:href="adam-20251231.xsd#adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:to="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesPerRSU" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount_edd630f0-7c46-4541-939f-609dac7e1c24_terseLabel_en-US" xlink:label="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum Committed Mortgage Principal Amount</link:label>
    <link:label id="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount_label_en-US" xlink:label="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long Term Debt, Maximum Committed Mortgage Principal Amount</link:label>
    <link:label id="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount_documentation_en-US" xlink:label="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Long Term Debt, Maximum Committed Mortgage Principal Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:href="adam-20251231.xsd#adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:to="lab_adam_LongTermDebtMaximumCommittedMortgagePrincipalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_019c41b7-b5e0-7930-88bf-f868691848ec_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsAxis"/>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateFaceAmountOfMortgages_4911cb31-10b1-4f3a-8c48-492298debffb_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateFaceAmountOfMortgages" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateFaceAmountOfMortgages_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateFaceAmountOfMortgages" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Face Amount of Mortgages</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateFaceAmountOfMortgages" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateFaceAmountOfMortgages"/>
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    <link:label id="lab_adam_BaltimoreMDMember_eca84eb1-cc40-4138-bfb8-0fda54c1125e_terseLabel_en-US" xlink:label="lab_adam_BaltimoreMDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Baltimore, MD</link:label>
    <link:label id="lab_adam_BaltimoreMDMember_label_en-US" xlink:label="lab_adam_BaltimoreMDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Baltimore, MD [Member]</link:label>
    <link:label id="lab_adam_BaltimoreMDMember_documentation_en-US" xlink:label="lab_adam_BaltimoreMDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Baltimore, MD</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_66abe64c-8698-418d-bdb1-24e627d43a40_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Other Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfOtherAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfOtherAssetsTableTextBlock"/>
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    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
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    <link:label id="lab_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss_4fdcecca-c4e7-40e4-9186-85a80601aa7a_negatedLabel_en-US" xlink:label="lab_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net impairment loss</link:label>
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    <link:label id="lab_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss_documentation_en-US" xlink:label="lab_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment of Real Estate, Recovery Impairment Gain (loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss" xlink:href="adam-20251231.xsd#adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss" xlink:to="lab_adam_ImpairmentOfRealEstateRecoveryImpairmentGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_ebf76d4f-2dc0-4645-95f1-2e2adfee56ea_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET INCOME (LOSS) ATTRIBUTABLE TO COMPANY'S COMMON STOCKHOLDERS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_002fa06c-63b0-4237-98fd-e2230c586862_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">NET INCOME (LOSS) ATTRIBUTABLE TO COMPANY'S COMMON STOCKHOLDERS</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing_0452d5d0-e462-4f37-aab4-78f87031c1f4_terseLabel_en-US" xlink:label="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan origination and other fees</link:label>
    <link:label id="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing_019c2f9d-4878-7e31-be25-01cf9c83f617_verboseLabel_en-US" xlink:label="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Servicing fee income</link:label>
    <link:label id="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing_label_en-US" xlink:label="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fees and Commissions, Mortgage Banking and Servicing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeesAndCommissionsMortgageBankingAndServicing"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:to="lab_us-gaap_FeesAndCommissionsMortgageBankingAndServicing" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_cc2f8bce-78e6-4705-82c8-c95dc29af5f8_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">TOTAL OTHER COMPREHENSIVE INCOME</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_019bf84d-4f6a-70e9-bfcd-cbf2a69191b7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest prior to business combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Achieved in Stages, Preacquisition Equity Interest in Acquiree, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:to="lab_us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstate_7ca94b9f-06c2-418a-af05-69211fec7dfc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total gross proceeds</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstate_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfRealEstate" xlink:to="lab_us-gaap_ProceedsFromSaleOfRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AgencyRMBSMember_019c22d9-e430-76c4-9ca7-74b2813d7d1f_terseLabel_en-US" xlink:label="lab_adam_AgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Agency RMBS</link:label>
    <link:label id="lab_adam_AgencyRMBSMember_label_en-US" xlink:label="lab_adam_AgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency RMBS [Member]</link:label>
    <link:label id="lab_adam_AgencyRMBSMember_documentation_en-US" xlink:label="lab_adam_AgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency RMBS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AgencyRMBSMember" xlink:href="adam-20251231.xsd#adam_AgencyRMBSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AgencyRMBSMember" xlink:to="lab_adam_AgencyRMBSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember_f6e7bfb3-18ba-4183-b932-eb2faf5cf4e9_terseLabel_en-US" xlink:label="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate, Excluding Held For Sale</link:label>
    <link:label id="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember_label_en-US" xlink:label="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate, Excluding Held For Sale [Member]</link:label>
    <link:label id="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Operating Real Estate, Excluding Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_TotalOperatingRealEstateExcludingHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:to="lab_adam_TotalOperatingRealEstateExcludingHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NumberOfRealEstatePropertiesSold_27aeec85-3071-480e-85b0-975a58b869c0_terseLabel_en-US" xlink:label="lab_adam_NumberOfRealEstatePropertiesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of real estate properties sold</link:label>
    <link:label id="lab_adam_NumberOfRealEstatePropertiesSold_label_en-US" xlink:label="lab_adam_NumberOfRealEstatePropertiesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties Sold</link:label>
    <link:label id="lab_adam_NumberOfRealEstatePropertiesSold_documentation_en-US" xlink:label="lab_adam_NumberOfRealEstatePropertiesSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NumberOfRealEstatePropertiesSold" xlink:href="adam-20251231.xsd#adam_NumberOfRealEstatePropertiesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NumberOfRealEstatePropertiesSold" xlink:to="lab_adam_NumberOfRealEstatePropertiesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_294d8e5f-02a9-4aff-b65a-b390d45a1dca_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total general, administrative and operating expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_98afa2da-647f-4e86-b3b5-3937c002682b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans_28a127d2-c7b2-4318-b576-06ee49ddfa3f_verboseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Multi-family loans</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans_label_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Multi-family Loans</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans_documentation_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Multi-family Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:href="adam-20251231.xsd#adam_FinancialInstrumentsOwnedMultiFamilyLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:to="lab_adam_FinancialInstrumentsOwnedMultiFamilyLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_c26c15d3-3a4e-48f5-a1df-cf5b552855dc_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Redemption Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockRedemptionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:to="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_e95112fc-7959-4ed2-92cb-1eb9a000356c_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted earnings (loss) per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_b1e77abc-a38e-4fdf-a5c2-6bc7d4b11506_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted Loss per Common Share (in USD per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RentalIncomeOperating_8d90a4fc-f1bd-43be-9fb5-c1485540a780_totalLabel_en-US" xlink:label="lab_adam_RentalIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income from real estate</link:label>
    <link:label id="lab_adam_RentalIncomeOperating_label_en-US" xlink:label="lab_adam_RentalIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rental Income, Operating</link:label>
    <link:label id="lab_adam_RentalIncomeOperating_documentation_en-US" xlink:label="lab_adam_RentalIncomeOperating" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Rental Income, Operating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RentalIncomeOperating" xlink:href="adam-20251231.xsd#adam_RentalIncomeOperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RentalIncomeOperating" xlink:to="lab_adam_RentalIncomeOperating" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale_019b921f-3412-7781-be68-cdd688cb706f_terseLabel_en-US" xlink:label="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales Proceeds</link:label>
    <link:label id="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale_label_en-US" xlink:label="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds Including Receivable For Unsettled Trades From Sale of Debt Securities, Available-for-sale</link:label>
    <link:label id="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale_documentation_en-US" xlink:label="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds Including Receivable For Unsettled Trades From Sale of Debt Securities, Available-for-sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:href="adam-20251231.xsd#adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:to="lab_adam_ProceedsIncludingReceivableForUnsettledTradesFromSaleofDebtSecuritiesAvailableforsale" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MultifamilyMember_faf14d1c-0704-4818-82ed-dfc8b438f185_terseLabel_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-Family - Operating</link:label>
    <link:label id="lab_srt_MultifamilyMember_label_en-US" xlink:label="lab_srt_MultifamilyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multifamily [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MultifamilyMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MultifamilyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MultifamilyMember" xlink:to="lab_srt_MultifamilyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateByLoanDisclosureTextBlock_3271734b-8f70-407d-ba10-d14ecfe33e24_netLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateByLoanDisclosureTextBlock" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Schedule IV - Mortgage Loans on Real Estate</link:label>
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    <link:label id="lab_us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure_689d457b-2b08-49a5-a017-bf1556400f26_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsHeldForSaleLongLivedFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019c2f12-50e3-7cf7-95d2-3365071147d6_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 5 to 10 years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
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    <link:label id="lab_adam_OtherLossIncomeMiscellaneous_2f9918f8-9d20-487f-84db-85627d16b720_terseLabel_en-US" xlink:label="lab_adam_OtherLossIncomeMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Miscellaneous</link:label>
    <link:label id="lab_adam_OtherLossIncomeMiscellaneous_label_en-US" xlink:label="lab_adam_OtherLossIncomeMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other (Loss) Income Miscellaneous</link:label>
    <link:label id="lab_adam_OtherLossIncomeMiscellaneous_documentation_en-US" xlink:label="lab_adam_OtherLossIncomeMiscellaneous" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other (Loss) Income Miscellaneous</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OtherLossIncomeMiscellaneous" xlink:href="adam-20251231.xsd#adam_OtherLossIncomeMiscellaneous"/>
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    <link:label id="lab_us-gaap_DividendsPreferredStockCash_d4b6854f-c37c-4f7f-993c-a54461199883_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared on preferred stock</link:label>
    <link:label id="lab_us-gaap_DividendsPreferredStockCash_label_en-US" xlink:label="lab_us-gaap_DividendsPreferredStockCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends, Preferred Stock, Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPreferredStockCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPreferredStockCash"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPreferredStockCash" xlink:to="lab_us-gaap_DividendsPreferredStockCash" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_6f03d3d1-4bd3-45b8-a115-0211cb439381_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Servicing Asset, Fair Value, Change in Fair Value, Other, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset, Fair Value, Change in Fair Value, Other, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueOtherChangeInFairValueStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration"/>
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    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_019c2c56-a57a-7558-93ce-1f9b2a37798f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">States</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, State and Local, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived"/>
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    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationLineItems_cb8dc6c0-7547-49b9-aa19-70134fb655dd_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate properties and accumulated depreciation</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationLineItems_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:to="lab_srt_RealEstateAndAccumulatedDepreciationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019bf8a6-7dd6-785c-9f04-cd83dac2376a_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_318b6c16-7127-4064-8d36-3dd48d88cdf9_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:label id="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Debt and Equity Securities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:to="lab_us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_8f4425ba-b1bd-4569-b717-a85020d5848c_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_5c94a7c8-7cde-4528-8a49-2ee6a52e7418_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Not Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityNotPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAdditions_a731128d-9ab1-4a0b-86c7-3858ed3f189a_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of MSRs</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAdditions_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Additions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAdditions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueAdditions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAdditions" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAdditions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_b2befcc0-94e3-49d3-b61e-71950fed3466_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Investments, at Fair Value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationMember_55be9343-a169-48a4-a7a9-341319d1e05d_terseLabel_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS re-securitization</link:label>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationMember_label_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS Re-Securitization [Member]</link:label>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationMember_documentation_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS Re-Securitization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NonAgencyRMBSReSecuritizationMember" xlink:href="adam-20251231.xsd#adam_NonAgencyRMBSReSecuritizationMember"/>
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    <link:label id="lab_adam_ChicagoILMember_69e474a1-669e-4717-88f0-4c2113b335c3_terseLabel_en-US" xlink:label="lab_adam_ChicagoILMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Chicago, IL</link:label>
    <link:label id="lab_adam_ChicagoILMember_label_en-US" xlink:label="lab_adam_ChicagoILMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Chicago, IL [Member]</link:label>
    <link:label id="lab_adam_ChicagoILMember_documentation_en-US" xlink:label="lab_adam_ChicagoILMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Chicago, IL</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ChicagoILMember" xlink:href="adam-20251231.xsd#adam_ChicagoILMember"/>
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    <link:label id="lab_adam_DebtInstrumentInterestRateIncreasesMonthsAfterIssuance_7d5beadb-b40d-4b3c-9b3e-155be57e6ebb_terseLabel_en-US" xlink:label="lab_adam_DebtInstrumentInterestRateIncreasesMonthsAfterIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, interest rate increases, months after issuance</link:label>
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    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_019c4e34-6d4d-7c90-803e-5aa25cc26d59_negatedLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Common and preferred stock repurchases</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_019c4e33-8786-736f-9440-f29806f05d58_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased, value</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Value</link:label>
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    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo_a96d189f-958a-4f8f-8bc9-6690844c8393_terseLabel_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo_documentation_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo" xlink:href="adam-20251231.xsd#adam_RealEstateInvestmentPropertyExpectedDepreciationYearTwo"/>
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    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_ee49fae0-507f-45fc-b8f2-4b87e5de6bab_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomePolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:to="lab_us-gaap_ComprehensiveIncomePolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NoncashOrPartNoncashAcquisitionConsideration_019c224e-725a-7011-840f-4becba3246d7_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashAcquisitionConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-cash consideration for acquisition of business</link:label>
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    <link:label id="lab_adam_NoncashOrPartNoncashAcquisitionConsideration_documentation_en-US" xlink:label="lab_adam_NoncashOrPartNoncashAcquisitionConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash Or Part Noncash Acquisition, Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NoncashOrPartNoncashAcquisitionConsideration" xlink:href="adam-20251231.xsd#adam_NoncashOrPartNoncashAcquisitionConsideration"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_64885b40-d303-4766-9bac-eb4aae698b07_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
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    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_6af06e5e-bc2e-409d-a860-0c9824c0402b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid (refunds received) for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019c2c6d-5d0c-7da7-b2fc-e6ffe3615326_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash paid (refunds received) for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis_ccf72e4a-cf9d-41df-b052-dd86c11f6ff7_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents [Axis]</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalents [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock_fd529fbf-3325-4cc3-819e-33d07cc57ccf_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of DSU Award Activity</link:label>
    <link:label id="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock_label_en-US" xlink:label="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule &#8203;Of &#8203;Nonvested&#8203; Deferred Stock &#8203;Units &#8203;Activity &#8203; [Table Text Block]</link:label>
    <link:label id="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock_documentation_en-US" xlink:label="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule &#8203;Of &#8203;Nonvested&#8203; Deferred Stock &#8203;Units &#8203;Activity &#8203;</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:to="lab_adam_ScheduleOfNonvestedDeferredStockUnitsActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019bf84d-4f6a-72e3-a6dc-71238c0372a6_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent_0326351b-1659-4036-9013-d7edac7f3cb1_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SwapMaturities2034Member_062a2201-1a0b-465b-a4dc-5c3f33e8ebbc_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2034Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2034</link:label>
    <link:label id="lab_adam_SwapMaturities2034Member_label_en-US" xlink:label="lab_adam_SwapMaturities2034Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swap Maturities 2034 [Member]</link:label>
    <link:label id="lab_adam_SwapMaturities2034Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2034Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2034</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2034Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2034Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SwapMaturities2034Member" xlink:to="lab_adam_SwapMaturities2034Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_4cbc828e-1521-447a-a6f2-43a0f8206159_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_fa5b3ba1-033f-4b09-8bb4-88d63d887d7e_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_24ce48bf-9abf-435b-b495-db962c0b7b6a_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Mortgage Balance</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember_e82ffe5e-eca1-4695-b47e-b78ba0016d91_terseLabel_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS Re-Securitization At Fair Value</link:label>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember_label_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS Re-Securitization At Fair Value [Member]</link:label>
    <link:label id="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember_documentation_en-US" xlink:label="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS Re-Securitization At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:href="adam-20251231.xsd#adam_NonAgencyRMBSReSecuritizationAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:to="lab_adam_NonAgencyRMBSReSecuritizationAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_071dde43-d7e5-494f-a463-c05977277ea4_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember_10839bbd-84ba-4aad-914d-0ff1ccde5a13_terseLabel_en-US" xlink:label="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Unconsolidated Variable Interest Entities</link:label>
    <link:label id="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember_label_en-US" xlink:label="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Unconsolidated Variable Interest Entities [Member]</link:label>
    <link:label id="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember_documentation_en-US" xlink:label="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Unconsolidated Variable Interest Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:href="adam-20251231.xsd#adam_TotalUnconsolidatedVariableInterestEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:to="lab_adam_TotalUnconsolidatedVariableInterestEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_a14454aa-718d-4748-8e4e-a30e912c97e9_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total lease payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsShareBasedCompensation_d279fb78-0eac-41fa-9e74-6e3c9e5bffc5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DividendsShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends attributable to dividend equivalents</link:label>
    <link:label id="lab_us-gaap_DividendsShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_DividendsShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsShareBasedCompensation" xlink:to="lab_us-gaap_DividendsShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_b4c2343f-e3ae-4dee-bbac-e5794ba460f3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in fair value of available for sale securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_755409c5-3601-4005-83e3-3b2915cc270b_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Increase in fair value of available for sale securities</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax"/>
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    <link:label id="lab_adam_VariableInterestEntityInitialConsolidationCashReceived_019c4e2f-bcdb-7080-b4e9-97d30b034339_terseLabel_en-US" xlink:label="lab_adam_VariableInterestEntityInitialConsolidationCashReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash received from initial consolidation of VIEs</link:label>
    <link:label id="lab_adam_VariableInterestEntityInitialConsolidationCashReceived_label_en-US" xlink:label="lab_adam_VariableInterestEntityInitialConsolidationCashReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Initial Consolidation, Cash Received</link:label>
    <link:label id="lab_adam_VariableInterestEntityInitialConsolidationCashReceived_documentation_en-US" xlink:label="lab_adam_VariableInterestEntityInitialConsolidationCashReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Initial Consolidation, Cash Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_VariableInterestEntityInitialConsolidationCashReceived" xlink:href="adam-20251231.xsd#adam_VariableInterestEntityInitialConsolidationCashReceived"/>
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    <link:label id="lab_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems_91142cec-51a4-4dfc-bd33-c4c98c39937f_terseLabel_en-US" xlink:label="lab_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]</link:label>
    <link:label id="lab_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems_label_en-US" xlink:label="lab_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsLineItems"/>
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    <link:label id="lab_us-gaap_DerivativeAssetMeasurementInput_019c2856-fbcf-7e6d-b020-e2c9819ffef0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative asset, measurement Input</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetMeasurementInput" xlink:to="lab_us-gaap_DerivativeAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_b32db564-2f28-4d44-a7c4-abd62f253782_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Decrease in non-controlling interest related to distributions from Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
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    <link:label id="lab_us-gaap_TradeNamesMember_019bf84d-4f6a-7021-bcca-a75bb511a9fe_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade name</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NumberOfEquityInvestmentsSold_66829467-1dd1-43b0-af55-02136648fe09_terseLabel_en-US" xlink:label="lab_adam_NumberOfEquityInvestmentsSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of equity investments sold</link:label>
    <link:label id="lab_adam_NumberOfEquityInvestmentsSold_label_en-US" xlink:label="lab_adam_NumberOfEquityInvestmentsSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Equity Investments Sold</link:label>
    <link:label id="lab_adam_NumberOfEquityInvestmentsSold_documentation_en-US" xlink:label="lab_adam_NumberOfEquityInvestmentsSold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Equity Investments Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NumberOfEquityInvestmentsSold" xlink:href="adam-20251231.xsd#adam_NumberOfEquityInvestmentsSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NumberOfEquityInvestmentsSold" xlink:to="lab_adam_NumberOfEquityInvestmentsSold" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_GWRCedarsPartnersLLCMember_96a5ac65-9309-4e44-994d-3b5b973eba42_terseLabel_en-US" xlink:label="lab_adam_GWRCedarsPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GWR Cedars Partners, LLC</link:label>
    <link:label id="lab_adam_GWRCedarsPartnersLLCMember_label_en-US" xlink:label="lab_adam_GWRCedarsPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GWR Cedars Partners, LLC [Member]</link:label>
    <link:label id="lab_adam_GWRCedarsPartnersLLCMember_documentation_en-US" xlink:label="lab_adam_GWRCedarsPartnersLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GWR Cedars Partners, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_GWRCedarsPartnersLLCMember" xlink:href="adam-20251231.xsd#adam_GWRCedarsPartnersLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_GWRCedarsPartnersLLCMember" xlink:to="lab_adam_GWRCedarsPartnersLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_aeb460fb-6f98-43c6-90ea-21e83a8efca6_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Losses) gains on derivative instruments, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_b36fe12b-d73e-435b-a488-0b221552f3bb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Losses (gains) on derivative investments, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_3b4d9eec-894b-4e31-893d-aa7d17669ea7_netLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Gains on derivative instruments, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_019bf8a6-7dd6-7278-9c2b-eb02d02811d5_verboseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">(Losses) gains on derivative instruments, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax_label_en-US" xlink:label="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Derivative Instruments, Net, Pretax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnDerivativeInstrumentsNetPretax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:to="lab_us-gaap_GainLossOnDerivativeInstrumentsNetPretax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryRealEstatePolicy_bac1980d-2f6c-429a-9f21-c67d95585160_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRealEstatePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate - Impairment</link:label>
    <link:label id="lab_us-gaap_InventoryRealEstatePolicy_label_en-US" xlink:label="lab_us-gaap_InventoryRealEstatePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Real Estate, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRealEstatePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryRealEstatePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryRealEstatePolicy" xlink:to="lab_us-gaap_InventoryRealEstatePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember_34e7f470-e572-4063-9849-ddadc0a8a845_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Months to assumed redemption</link:label>
    <link:label id="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember_label_en-US" xlink:label="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Months To Assumed Redemption [Member]</link:label>
    <link:label id="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember_documentation_en-US" xlink:label="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input Months To Assumed Redemption</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputMonthsToAssumedRedemptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:to="lab_adam_MeasurementInputMonthsToAssumedRedemptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciation_85b8d2f5-0e64-4509-b0fa-9047205a987c_negatedLabel_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated Depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciation_6f51666c-3572-4add-a8bb-67132f5a4960_negatedPeriodStartLabel_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of period</link:label>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciation_a4b60a78-3806-488c-8767-5e72f863d67a_negatedPeriodEndLabel_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at end of period</link:label>
    <link:label id="lab_us-gaap_RealEstateAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_RealEstateAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAccumulatedDepreciation"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsTextBlock_c9c50bfe-8113-4a75-8b2f-bea6bd811356_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Measured on Recurring Basis, Gain (Loss) Included in Earnings</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsTextBlock"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_019bf84d-4f6a-78ef-9641-98816ed06945_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateCostOfRealEstateSold_bf20e2ef-e0d4-4a7f-9fc9-1972db7d128e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealEstateCostOfRealEstateSold" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification to held for sale or disposal group held for sale</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageVariableInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAverageVariableInterestRate"/>
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    <link:label id="lab_us-gaap_OtherInvestmentsMember_ca71e249-aa33-46ee-9e73-364da83c86af_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestmentsMember" xlink:to="lab_us-gaap_OtherInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_acb707d7-5078-4ffd-bd16-3451c473f2e1_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments in Unconsolidated Entities</link:label>
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    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_433cf736-65e7-495d-9f40-a89ada46b63a_terseLabel_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk</link:label>
    <link:label id="lab_us-gaap_GeographicConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_GeographicConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographic Concentration Risk [Member]</link:label>
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    <link:label id="lab_adam_CMETermSecuredOvernightFinancingRateMember_974d79c7-16ef-479d-a35e-ff3f9bfab049_terseLabel_en-US" xlink:label="lab_adam_CMETermSecuredOvernightFinancingRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CME Term, SOFR</link:label>
    <link:label id="lab_adam_CMETermSecuredOvernightFinancingRateMember_label_en-US" xlink:label="lab_adam_CMETermSecuredOvernightFinancingRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CME Term, Secured Overnight Financing Rate [Member]</link:label>
    <link:label id="lab_adam_CMETermSecuredOvernightFinancingRateMember_documentation_en-US" xlink:label="lab_adam_CMETermSecuredOvernightFinancingRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CME Term, Secured Overnight Financing Rate</link:label>
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    <link:label id="lab_dei_EntityCurrentReportingStatus_3293a9d8-f1d1-4948-878d-0dcf1ccc78de_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
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    <link:label id="lab_adam_A6875SeriesFFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_185fe579-566d-46e3-b8e3-5aabd359063d_terseLabel_en-US" xlink:label="lab_adam_A6875SeriesFFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">6.875% Series F Fixed-to-Floating Rate Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
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    <link:label id="lab_adam_A6875SeriesFFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_documentation_en-US" xlink:label="lab_adam_A6875SeriesFFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">6.875% Series F Fixed-to-Floating Rate Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
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    <link:label id="lab_us-gaap_DerivativeLineItems_71a7a367-3807-4c1b-be57-ccd254914c15_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLineItems" xlink:to="lab_us-gaap_DerivativeLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
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    <link:label id="lab_us-gaap_RealEstateHeldforsale_1729d72f-a6af-4ab4-882e-e63a6dcdb2e7_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate held for sale, net</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldforsale_label_en-US" xlink:label="lab_us-gaap_RealEstateHeldforsale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Held-for-Sale</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateHeldforsale" xlink:to="lab_us-gaap_RealEstateHeldforsale" xlink:type="arc" order="1"/>
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    <link:label id="lab_adam_PreferredStockVotingRightsNumberofAdditionalDirectorsElected_001e2511-a7d0-47ef-9072-b542c75467fd_terseLabel_en-US" xlink:label="lab_adam_PreferredStockVotingRightsNumberofAdditionalDirectorsElected" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of additional directors elected</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_46d30e88-73fd-4d92-833f-ded6f16850e4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision (benefit) at statutory rate</link:label>
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    <link:label id="lab_adam_AvailableForSaleSecuritiesPortfolioLife_8e4d279b-c467-4127-b1c5-e54e1005b50f_terseLabel_en-US" xlink:label="lab_adam_AvailableForSaleSecuritiesPortfolioLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average life of available for sale securities portfolio</link:label>
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    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_414ab360-794f-48b1-892d-60504320897e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
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    <link:label id="lab_adam_NumberOfSecuritizationsCompleted_label_en-US" xlink:label="lab_adam_NumberOfSecuritizationsCompleted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Securitizations Completed</link:label>
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    <link:label id="lab_adam_NumberOfSeriesOfCumulativeRedeemablePreferredStockOutstanding_a98033db-5524-4e10-91b5-5283d314007b_terseLabel_en-US" xlink:label="lab_adam_NumberOfSeriesOfCumulativeRedeemablePreferredStockOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of series of cumulative redeemable preferred stock outstanding</link:label>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_808e12c4-9453-48e2-99e2-3ee316eed0b8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTable"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_7ba21596-165a-4a80-b722-ba615bd78f08_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsInvestments_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Investments</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_1a99b293-ecfa-4971-88c5-b8689ba732b5_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate_cabd0e38-0acb-478b-98a8-abfde350c99c_terseLabel_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capitalization rate</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate_label_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Non-controlling Interest, Weighted Average Capitalization Rate</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate_documentation_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redeemable Non-controlling Interest, Weighted Average Capitalization Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate" xlink:href="adam-20251231.xsd#adam_RedeemableNonControllingInterestWeightedAverageCapitalizationRate"/>
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    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_f25c433a-9eab-4f04-8796-f14660f65d93_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AmericaWalksAtPortStLucieLLCMember_ae0d00fe-5c42-4b5f-a6af-d30d2b93defb_terseLabel_en-US" xlink:label="lab_adam_AmericaWalksAtPortStLucieLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">America Walks at Port St. Lucie, LLC</link:label>
    <link:label id="lab_adam_AmericaWalksAtPortStLucieLLCMember_label_en-US" xlink:label="lab_adam_AmericaWalksAtPortStLucieLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">America Walks at Port St. Lucie, LLC [Member]</link:label>
    <link:label id="lab_adam_AmericaWalksAtPortStLucieLLCMember_documentation_en-US" xlink:label="lab_adam_AmericaWalksAtPortStLucieLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">America Walks at Port St. Lucie, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AmericaWalksAtPortStLucieLLCMember" xlink:href="adam-20251231.xsd#adam_AmericaWalksAtPortStLucieLLCMember"/>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeNet_dce8179e-36a6-4586-912b-c8bc7e965992_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative asset, estimated fair value</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Fair Value, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeFairValueOfDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:to="lab_us-gaap_DerivativeFairValueOfDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MonroeGAMember_019c4747-2fa0-7689-b1d3-f914e31b82d7_terseLabel_en-US" xlink:label="lab_adam_MonroeGAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Monroe, GA</link:label>
    <link:label id="lab_adam_MonroeGAMember_label_en-US" xlink:label="lab_adam_MonroeGAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Monroe, GA [Member]</link:label>
    <link:label id="lab_adam_MonroeGAMember_documentation_en-US" xlink:label="lab_adam_MonroeGAMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Monroe, GA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MonroeGAMember" xlink:href="adam-20251231.xsd#adam_MonroeGAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MonroeGAMember" xlink:to="lab_adam_MonroeGAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_97d26be8-5c9b-4c31-96f8-f7a5e0d5a2ad_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_bd0bdb60-ccfe-4081-8d15-f0f39298746f_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining authorized repurchase amount</link:label>
    <link:label id="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1_label_en-US" xlink:label="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program, Remaining Authorized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:to="lab_us-gaap_StockRepurchaseProgramRemainingAuthorizedRepurchaseAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_51f8c227-f048-41b7-ba86-4341008500ce_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accrued Interest, after Allowance for Credit Loss, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLossStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_946b1381-d29f-4f11-8660-5394d8c722fb_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain" xlink:to="lab_us-gaap_DisposalGroupClassificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock_140eb57e-5633-406f-a4fa-5a671cba6a31_terseLabel_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule III - Real Estate and Accumulated Depreciation</link:label>
    <link:label id="lab_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock_label_en-US" xlink:label="lab_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate and Accumulated Depreciation Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock" xlink:to="lab_srt_RealEstateAndAccumulatedDepreciationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockOptionMember_9f328fca-43f1-4764-a45a-c1202502ad8b_terseLabel_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_StockOptionMember_574351e8-51b5-4877-b5d6-7650ef23d9ce_verboseLabel_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Options</link:label>
    <link:label id="lab_us-gaap_StockOptionMember_label_en-US" xlink:label="lab_us-gaap_StockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockOptionMember" xlink:to="lab_us-gaap_StockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
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    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract_4e66b4cd-632d-4dfe-8be6-8445036bf7ce_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amount at Close of Period</link:label>
    <link:label id="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract_label_en-US" xlink:label="lab_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Gross [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateAndAccumulatedDepreciationCarryingAmountOfLandAndBuildingsAndImprovementsAbstract"/>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_adam_A2030SeniorNotesMember_76be4278-59ab-41ff-92e2-1981a1a3469a_terseLabel_en-US" xlink:label="lab_adam_A2030SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030 Senior Notes</link:label>
    <link:label id="lab_adam_A2030SeniorNotesMember_label_en-US" xlink:label="lab_adam_A2030SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2030 Senior Notes [Member]</link:label>
    <link:label id="lab_adam_A2030SeniorNotesMember_documentation_en-US" xlink:label="lab_adam_A2030SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2030 Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A2030SeniorNotesMember" xlink:href="adam-20251231.xsd#adam_A2030SeniorNotesMember"/>
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    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_08b9c0fa-7dbe-4c97-88c5-2f81b7627fa9_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing transaction costs</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GranteeStatusAxis_14ef7674-051c-458b-a074-508c311764b2_terseLabel_en-US" xlink:label="lab_us-gaap_GranteeStatusAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Grantee Status [Axis]</link:label>
    <link:label id="lab_us-gaap_GranteeStatusAxis_label_en-US" xlink:label="lab_us-gaap_GranteeStatusAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Grantee Status [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GranteeStatusAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GranteeStatusAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GranteeStatusAxis" xlink:to="lab_us-gaap_GranteeStatusAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments_df197b19-c0e4-40e9-9e04-836001dc32e5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal repayments received on preferred equity and mezzanine loan investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:to="lab_us-gaap_ProceedsFromSaleOfEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_6637e4a1-4581-42d7-b20b-0ac74e8443e4_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flow</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanTypeAxis_c75dc84c-8786-41eb-849f-3761018798d0_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Type [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanTypeAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateLoanTypeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateLoanTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateLoanTypeAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateLoanTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_20ad8a37-8920-42a9-83d0-5f7cab5b44be_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Mezzanine Loans and Preferred Equity Investments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_75bc89f2-b985-4537-92c7-ccafc1149204_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_37aef7a8-9c9d-4f82-8a31-99bef5303a41_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of Properties</link:label>
    <link:label id="lab_us-gaap_NumberOfRealEstateProperties_label_en-US" xlink:label="lab_us-gaap_NumberOfRealEstateProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Real Estate Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfRealEstateProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfRealEstateProperties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfRealEstateProperties" xlink:to="lab_us-gaap_NumberOfRealEstateProperties" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy_34c72dfb-7bb5-4564-962e-a6c5b0cecfc1_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Benefits Plans</link:label>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy_label_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension and Other Postretirement Plans, Nonpension Benefits, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:to="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt_28357201-322c-4268-bbc0-61d2396b2810_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate in disposal group held for sale, carrying value</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt_label_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Long-Term Debt</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt_documentation_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet_0f1c8774-86e0-4f52-b9d0-e9f8e9d6a5b5_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate, net</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet_label_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Real Estate, Net</link:label>
    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet_documentation_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Real Estate, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationRealEstateNet" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember_9d86c397-4851-4865-acc2-596a86a03c02_verboseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held in securitization trusts</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans Held In Securitization Trust [Member]</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The amount of distressed mortgage loans held in a securitized trust.</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember" xlink:to="lab_adam_ResidentialMortgageLoansHeldInSecuritizationTrustMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_EquityDistributionAgreementsMember_830f56b7-3417-4524-9eea-8bcf9f687147_terseLabel_en-US" xlink:label="lab_adam_EquityDistributionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Distribution Agreements</link:label>
    <link:label id="lab_adam_EquityDistributionAgreementsMember_label_en-US" xlink:label="lab_adam_EquityDistributionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Distribution Agreements [Member]</link:label>
    <link:label id="lab_adam_EquityDistributionAgreementsMember_documentation_en-US" xlink:label="lab_adam_EquityDistributionAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Represents information pertaining to the separate equity distribution agreements (collectively, the "Equity Distribution Agreements") with each of JMP Securities LLC ("JMP") and MLV &amp; Co. LLC ("MLV").</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_EquityDistributionAgreementsMember" xlink:href="adam-20251231.xsd#adam_EquityDistributionAgreementsMember"/>
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    <link:label id="lab_us-gaap_CommonStockSharesIssued_6a7da79a-b369-48b2-8ac4-e847cbfd34cf_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration_6b039368-aafe-45a4-826d-b271bfca8130_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration" xlink:to="lab_us-gaap_DerivativeAssetStatementOfFinancialPositionExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_f8d808c4-5745-4b31-8c49-f1a2892d9978_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfOtherDerivativesNotDesignatedAsHedgingInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock_676b90c6-e4a2-4551-9c6d-e07204cc3549_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfOtherDerivativesNotDesignatedAsHedgingInstrumentsStatementsOfFinancialPerformanceAndFinancialPositionLocationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Activity of Derivatives Not Designated as Hedging Instruments</link:label>
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    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestTableTextBlock_b21dec3f-862c-4cbf-8ff1-346d3a00eafd_terseLabel_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Redeemable Noncontrolling Interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_RedeemableNoncontrollingInterestTableTextBlock_label_en-US" xlink:label="lab_us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Noncontrolling Interest [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RedeemableNoncontrollingInterestTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:to="lab_us-gaap_RedeemableNoncontrollingInterestTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance_019c22e9-374c-767a-93f4-39982ebec7f9_terseLabel_en-US" xlink:label="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal balance of loans originated</link:label>
    <link:label id="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance_label_en-US" xlink:label="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment For Origination, Loan, Mortgage, Held-For-Sale, Principal Balance</link:label>
    <link:label id="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance_documentation_en-US" xlink:label="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment For Origination, Loan, Mortgage, Held-For-Sale, Principal Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:href="adam-20251231.xsd#adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:to="lab_adam_PaymentForOriginationLoanMortgageHeldForSalePrincipalBalance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract_3e53044f-3439-4f5f-a7b1-5a62c440e18c_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current income tax provision</link:label>
    <link:label id="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract_label_en-US" xlink:label="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal, State and Local, Tax Expense (Benefit) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract" xlink:to="lab_us-gaap_CurrentFederalStateAndLocalTaxExpenseBenefitAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityPublicFloat_cfa30be3-a0f5-4466-b3ad-b1a6defdcbdc_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityPublicFloat"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityPublicFloat" xlink:to="lab_dei_EntityPublicFloat" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_019bf84d-4f6a-71ae-ad5b-bce84073c4be_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic proforma earnings (loss) per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_ec4dabc8-0185-44da-a9cd-c43a2fef7530_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesEPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesEPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series E Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesEPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesEPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesEPreferredStockMember" xlink:to="lab_us-gaap_SeriesEPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_66fb861d-7cdc-49a7-b4fb-e36c805c26c8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Included in earnings</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Gain (Loss) Included in Earnings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityGainLossIncludedInEarnings" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_814bf92c-27df-4530-aba8-7799b8dd6082_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Type of Property [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:to="lab_srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019bf8a6-7dd6-7d49-8df3-1b1adab6adb2_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate/Other</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_bc9fd3a2-ffbe-4e36-8c3c-907741ddf954_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MontgomeryALMember_fff77d43-62c7-4325-aaaf-cbb4ec43aeb1_terseLabel_en-US" xlink:label="lab_adam_MontgomeryALMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Montgomery, AL</link:label>
    <link:label id="lab_adam_MontgomeryALMember_label_en-US" xlink:label="lab_adam_MontgomeryALMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Montgomery, AL [Member]</link:label>
    <link:label id="lab_adam_MontgomeryALMember_documentation_en-US" xlink:label="lab_adam_MontgomeryALMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Montgomery, AL</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MontgomeryALMember" xlink:href="adam-20251231.xsd#adam_MontgomeryALMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MontgomeryALMember" xlink:to="lab_adam_MontgomeryALMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseIncome_684075ed-6f98-45ea-804f-d179ecc736a8_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rental income</link:label>
    <link:label id="lab_us-gaap_LeaseIncome_label_en-US" xlink:label="lab_us-gaap_LeaseIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseIncome" xlink:to="lab_us-gaap_LeaseIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold_ecc1dfc2-c423-4c06-8b78-43d97bb152ff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cost of loans sold</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Cost of Mortgage Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold" xlink:to="lab_us-gaap_MortgageLoansOnRealEstateCostOfMortgagesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue_046a9798-611e-443a-aa66-503fa7d3de00_verboseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans:</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue_label_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Residential Loans at Fair Value</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue_documentation_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Residential Loans at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:href="adam-20251231.xsd#adam_FinancialInstrumentsOwnedResidentialLoansatFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:to="lab_adam_FinancialInstrumentsOwnedResidentialLoansatFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SwapMaturities2033Member_c77431e3-c7eb-4ef6-958c-0802032f0336_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2033Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2033</link:label>
    <link:label id="lab_adam_SwapMaturities2033Member_label_en-US" xlink:label="lab_adam_SwapMaturities2033Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swap Maturities 2033 [Member]</link:label>
    <link:label id="lab_adam_SwapMaturities2033Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2033Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2033</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2033Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2033Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SwapMaturities2033Member" xlink:to="lab_adam_SwapMaturities2033Member" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLineItems_172bfee6-53a0-4fdd-8f14-dc6c37c96b8c_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate [Line Items]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLineItems_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateLineItems" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateLineItems" xlink:to="lab_srt_MortgageLoansOnRealEstateLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AuditorInformationAbstract_label_en-US" xlink:label="lab_adam_AuditorInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Information [Abstract]</link:label>
    <link:label id="lab_adam_AuditorInformationAbstract_documentation_en-US" xlink:label="lab_adam_AuditorInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Auditor Information</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AuditorInformationAbstract" xlink:href="adam-20251231.xsd#adam_AuditorInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AuditorInformationAbstract" xlink:to="lab_adam_AuditorInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_cdadf87c-8623-4e47-8a7a-b79f14a7c3e4_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedDuringPeriodShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockRepurchasedDuringPeriodShares" xlink:to="lab_us-gaap_StockRepurchasedDuringPeriodShares" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember_688a5c04-dd3d-4545-9575-823fff4043be_terseLabel_en-US" xlink:label="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS re-securitization</link:label>
    <link:label id="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember_label_en-US" xlink:label="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non Agency RMBS and CMBS Re-Securitizations [Member]</link:label>
    <link:label id="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember_documentation_en-US" xlink:label="lab_adam_NonAgencyRMBSAndCMBSReSecuritizationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non Agency RMBS and CMBS Re-Securitizations</link:label>
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    <link:label id="lab_us-gaap_StatementLineItems_60f1f914-16a7-4649-b643-bd1dece1edd3_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PreferredStockCurrentDividendRatePercentage_019be54e-5bbb-76c6-9c9b-3a62d2f025c9_terseLabel_en-US" xlink:label="lab_adam_PreferredStockCurrentDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rate as of Period End</link:label>
    <link:label id="lab_adam_PreferredStockCurrentDividendRatePercentage_label_en-US" xlink:label="lab_adam_PreferredStockCurrentDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Current Dividend Rate, Percentage</link:label>
    <link:label id="lab_adam_PreferredStockCurrentDividendRatePercentage_documentation_en-US" xlink:label="lab_adam_PreferredStockCurrentDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Current Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredStockCurrentDividendRatePercentage" xlink:href="adam-20251231.xsd#adam_PreferredStockCurrentDividendRatePercentage"/>
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    <link:label id="lab_adam_RealEstateHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_RealEstateHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_RealEstateHeldForSaleMember"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_1a4eee0c-5758-4afb-a21a-8b8bed8d6a88_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_18bed9ce-6630-49fd-a678-0fbd2b606427_netLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_5274b971-045a-4d9e-ac6f-067f78e9697a_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
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    <link:label id="lab_us-gaap_SubsequentEventLineItems_label_en-US" xlink:label="lab_us-gaap_SubsequentEventLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventLineItems" xlink:to="lab_us-gaap_SubsequentEventLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_3b85679b-2ee2-4b86-bf8a-685439d97c7d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_0b341d42-41b4-4792-96e7-d8b50e142a57_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_cc58efeb-1e0b-42cc-a063-3035ba76178c_negatedLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period</link:label>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_d211519d-e09c-4d6f-9a8c-bd8012655af4_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsIntangibleAssetsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Intangible Assets, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation_d4acdd44-bc1b-4355-9208-4d383cb53fdb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated depreciation</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Accumulated Depreciation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyAccumulatedDepreciation"/>
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    <link:label id="lab_adam_ResidentialLoansHeldinSecuritizationTrustsMember_662c0be6-4972-4df6-9f54-41d1b1027198_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansHeldinSecuritizationTrustsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held in securitization trusts</link:label>
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    <link:label id="lab_adam_ToBeAnnouncedSecuritiesMember_019c283d-8e02-7455-a938-979e27eb4fb8_terseLabel_en-US" xlink:label="lab_adam_ToBeAnnouncedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">TBAs</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputPrepaymentRateMember_5a0a6d7f-4201-4b47-b7d6-d2c463f29c12_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPrepaymentRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lifetime voluntary prepayment rate</link:label>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareCashPaid_99e4cb21-3cdd-4fde-bf39-c2c6405e8f1e_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid (USD per share)</link:label>
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    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_6d99b9b5-1ec0-4966-b02d-11c4ea92d65d_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses), net</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_061f8b54-0cf5-4d9c-b9e4-8def69989768_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (gains) losses, net</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_b376ba9a-0f77-4c90-957a-6d5fd353f41b_verboseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unrealized (losses) gains, net</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestments"/>
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    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_59950e9d-6eb6-4d3d-8dd2-35dc6735de8b_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PreferredEquityAndMezzanineLoansAccumulatedGrossUnrealizedGainLossBeforeTax_d38ecd0f-e715-4c4c-880d-c7b7f54b5bb7_terseLabel_en-US" xlink:label="lab_adam_PreferredEquityAndMezzanineLoansAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses, net</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredEquityAndMezzanineLoansAccumulatedGrossUnrealizedGainLossBeforeTax" xlink:href="adam-20251231.xsd#adam_PreferredEquityAndMezzanineLoansAccumulatedGrossUnrealizedGainLossBeforeTax"/>
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    <link:label id="lab_adam_BighausLLCMember_3dfbd5a3-b9a7-4a37-8ca9-da4e39c6b5cf_terseLabel_en-US" xlink:label="lab_adam_BighausLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bighaus, LLC</link:label>
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    <link:label id="lab_srt_RangeMember_458b0c1e-9420-4305-88dd-a9526c9e79cb_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive_9b5abdda-1b69-49ff-b1fa-5a9fd8122d54_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock_22dbda52-253b-4fc7-aca6-2aa3f6bf555e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNotionalAmountsOfOutstandingDerivativePositionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Cap Contracts Strike Price and Notional Amounts</link:label>
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    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateOriginationsOfResidentialLoansHeldForSale_019c41e8-8ca6-7d2d-8e8c-4063306fbe7d_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateOriginationsOfResidentialLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Originations of residential loans held for sale</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfNonvestedPerformanceBasedUnitsActivityTableTextBlock_8c8268e2-a771-4c5e-8ce4-0aec745b4043_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNonvestedPerformanceBasedUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of PSU Award Activity</link:label>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanCategoryDomain_afe3f3a0-0c22-4248-a793-f7ffbb0cf841_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Category [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanCategoryDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanCategoryDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Category [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateLoanCategoryDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateLoanCategoryDomain"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_394a92d0-fdfe-4a28-9bf1-3abb3bd25f5d_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_158e8285-82cd-47de-86b1-a89f6b0f505d_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeDomain" xlink:to="lab_us-gaap_MeasurementInputTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToNoncontrollingInterestBeforeIncomeTax_c0d281b7-9df0-4e5b-bee8-eb5d8fe80e02_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToNoncontrollingInterestBeforeIncomeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Pretax loss of disposal group attributable to non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToNoncontrollingInterestBeforeIncomeTax_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromIndividuallySignificantComponentDisposedOfOrHeldForSaleExcludingDiscontinuedOperationsAttributableToNoncontrollingInterestBeforeIncomeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Individually Significant Component Disposed of or Held-for-Sale, Excluding Discontinued Operations, Attributable to Noncontrolling Interest, before Income Tax</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock_8725186c-c040-4dc0-b29a-b8fbacf5f535_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities Reconciliation</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-Sale Securities Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock"/>
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    <link:label id="lab_adam_TaxableREITSubsidiariesMember_197daa47-9259-4a4e-b07b-fa9015fc0bef_terseLabel_en-US" xlink:label="lab_adam_TaxableREITSubsidiariesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Taxable REIT Subsidiaries</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_2c98cffc-8b13-4ebb-b6d4-cb5e8ca6ea15_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses)</link:label>
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    <link:label id="lab_adam_PittsburghPAMember_d5d35665-7d8b-440c-8f62-82ad3138d62e_terseLabel_en-US" xlink:label="lab_adam_PittsburghPAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pittsburgh, PA</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromDivestitureOfInterestInJointVenture_0fa1d1bc-55fa-41c3-a42d-62b447aa0577_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromDivestitureOfInterestInJointVenture" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of joint venture equity investments in VIEs</link:label>
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    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationLossGainOnWriteDown_e1f852e1-f6e9-4667-af8c-cf94ef30baf8_negatedLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationLossGainOnWriteDown" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Loss on reclassification of disposal group</link:label>
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    <link:label id="lab_adam_RentalIncomeExcludingOtherRealEstateIncome_a86b366a-c9a7-473c-a04a-fabf27e741c9_terseLabel_en-US" xlink:label="lab_adam_RentalIncomeExcludingOtherRealEstateIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rental income</link:label>
    <link:label id="lab_adam_RentalIncomeExcludingOtherRealEstateIncome_label_en-US" xlink:label="lab_adam_RentalIncomeExcludingOtherRealEstateIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rental Income, Excluding Other Real Estate Income</link:label>
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    <link:label id="lab_adam_NumberOfCounterpartiesWithAmountsOutstandingUnderRepurchaseAgreements_0f5c9ea8-8508-430b-ad8d-9b5187f5edc7_terseLabel_en-US" xlink:label="lab_adam_NumberOfCounterpartiesWithAmountsOutstandingUnderRepurchaseAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of counterparties with amounts outstanding under repurchase agreements</link:label>
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    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_a5a77d03-d8a8-4459-b84d-40695f07741e_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">VIE, Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesSubscribedButUnissuedValue_b1c94b1e-4f6f-44c4-a044-d402986dd7b3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesSubscribedButUnissuedValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity agreement for preferred stock maximum aggregate sales price (up to)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesSubscribedButUnissuedValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesSubscribedButUnissuedValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Subscriptions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesSubscribedButUnissuedValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockSharesSubscribedButUnissuedValue"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_cf23e9aa-37a7-4d1e-a091-101ff0a16d9b_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Funding of preferred equity, mezzanine loan and equity investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
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    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationDomain"/>
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    <link:label id="lab_us-gaap_SecuredDebt_52120ebf-dea4-4e1b-b6d5-7743e132aa8f_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations ($3,148,157 at fair value and $363,645 at amortized cost, net as of December&#160;31, 2025 and $2,135,680 at fair value and $842,764 at amortized cost, net as of December&#160;31, 2024)</link:label>
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    <link:label id="lab_us-gaap_SecuredDebt_01ea44cb-d5e0-497d-9763-2da7d4c57967_netLabel_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_SecuredDebt_label_en-US" xlink:label="lab_us-gaap_SecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SecuredDebt"/>
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    <link:label id="lab_adam_DeferredTaxAssetsResidentialLoans_019c2ea3-419d-71ae-a0c8-b7134b5d3a6d_terseLabel_en-US" xlink:label="lab_adam_DeferredTaxAssetsResidentialLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateRepurchase_019c41e5-8fff-7108-940b-7288846deb01_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchases</link:label>
    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateRepurchase_label_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Repurchase</link:label>
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    <link:label id="lab_adam_RestrictedCashMember_32981154-d5c2-4e61-b659-00f8871b94d9_terseLabel_en-US" xlink:label="lab_adam_RestrictedCashMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_adam_RestrictedCashMember_label_en-US" xlink:label="lab_adam_RestrictedCashMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash [Member]</link:label>
    <link:label id="lab_adam_RestrictedCashMember_documentation_en-US" xlink:label="lab_adam_RestrictedCashMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RestrictedCashMember" xlink:href="adam-20251231.xsd#adam_RestrictedCashMember"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOther"/>
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    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_a88d6316-3f94-4883-acde-4b13691a3111_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
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    <link:label id="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_3122a042-7d7b-4ca7-9795-81c53afcaafe_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate increase</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets_label_en-US" xlink:label="lab_us-gaap_SegmentExpenditureAdditionToLongLivedAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment, Expenditure, Addition to Long-Lived Assets</link:label>
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    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_a2c8403f-f04e-4e4e-8359-78b24967cc53_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_e5273105-fa80-4d07-9c7d-e5d42ca175b3_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_b60a2795-6c5e-42a4-8cbf-f7db6a4cc69a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of shares vested</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value</link:label>
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    <link:label id="lab_us-gaap_DividendsPayableLineItems_c2111afe-1af5-43c5-a7be-8940d003209a_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends Payable [Line Items]</link:label>
    <link:label id="lab_us-gaap_DividendsPayableLineItems_label_en-US" xlink:label="lab_us-gaap_DividendsPayableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable [Line Items]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableLineItems" xlink:to="lab_us-gaap_DividendsPayableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanTypeDomain_9ba788aa-6ca5-4d3a-9986-0d8e67bbb3d5_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Type [Domain]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateLoanTypeDomain_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateLoanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Loan Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateLoanTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateLoanTypeDomain"/>
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    <link:label id="lab_us-gaap_CollateralizedDebtObligationsMember_f2eb9875-6378-4e7d-b8e8-9e048ee08b91_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiability_cc21cc51-6a99-480a-a554-ce1b5f826b19_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_6e89f115-8cf3-47ac-b1f9-6a2d258a73c5_verboseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Present value of lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_066c3925-8655-4667-9eb3-c71b0e9fd63d_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CDOs:</link:label>
    <link:label id="lab_us-gaap_LoansPayableFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansPayableFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayableFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayableFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_22df5a9a-bf53-45d2-a769-c02cda8fe6db_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Greater than 90 days past due</link:label>
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    <link:label id="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
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    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_6fe51162-b03b-4adf-a58b-2c73e51d4af4_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation preference (USD per share)</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_7befda9d-1527-41d4-bdf9-73c467a2d8ad_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019bf84d-4f6a-7934-b0ca-bb86e6148a68_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateAbstract_42cfbece-97f3-43a5-b237-f7a798c252df_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate [Abstract]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateAbstract_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateAbstract" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateAbstract" xlink:to="lab_srt_MortgageLoansOnRealEstateAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableSale_019b923d-fb6b-7b1b-82ca-989efdb06602_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of residential loans</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableSale_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancingReceivableSale" xlink:to="lab_us-gaap_FinancingReceivableSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstatePolicyTextBlock_94c2c5fb-8a6a-4725-98a2-381626e2bff7_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstatePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate, Net</link:label>
    <link:label id="lab_us-gaap_RealEstatePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RealEstatePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstatePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstatePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstatePolicyTextBlock" xlink:to="lab_us-gaap_RealEstatePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions_a77ba3de-150e-4909-b33e-b16db4c8343b_terseLabel_en-US" xlink:label="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funding/Contributions</link:label>
    <link:label id="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions_label_en-US" xlink:label="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Contributions</link:label>
    <link:label id="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions_documentation_en-US" xlink:label="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Contributions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:href="adam-20251231.xsd#adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:to="lab_adam_FairValueMeasurementwithUnobservableInputsReconciliationRecurringBasisAssetContributions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy_273813a6-67e2-4e6f-87a4-84cc65750be5_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Held for Sale Determination and Real Estate Sales</link:label>
    <link:label id="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy_label_en-US" xlink:label="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Held for Development and Sale, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateHeldForDevelopmentAndSalePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:to="lab_us-gaap_RealEstateHeldForDevelopmentAndSalePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageLoansBetween100000199999Member_8db41f5e-4af7-4c23-85a9-5a75d4e77601_terseLabel_en-US" xlink:label="lab_adam_MortgageLoansBetween100000199999Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans Between $100,000 - $199,999</link:label>
    <link:label id="lab_adam_MortgageLoansBetween100000199999Member_label_en-US" xlink:label="lab_adam_MortgageLoansBetween100000199999Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans Between $100,000 - $199,999 [Member]</link:label>
    <link:label id="lab_adam_MortgageLoansBetween100000199999Member_documentation_en-US" xlink:label="lab_adam_MortgageLoansBetween100000199999Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans Between $100,000 - $199,999</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageLoansBetween100000199999Member" xlink:href="adam-20251231.xsd#adam_MortgageLoansBetween100000199999Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MortgageLoansBetween100000199999Member" xlink:to="lab_adam_MortgageLoansBetween100000199999Member" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld_b301666d-ab62-43fc-904e-1b8dfeffc9dc_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">De-consolidation of real estate held in Consolidated VIEs</link:label>
    <link:label id="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld_label_en-US" xlink:label="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Disposition, De-Consolidation Of Real Estate Held</link:label>
    <link:label id="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld_documentation_en-US" xlink:label="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Disposition, De-Consolidation Of Real Estate Held</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:href="adam-20251231.xsd#adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:to="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfRealEstateHeld" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_58300938-fcc3-4ceb-9634-16dfda27547d_negatedTerseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repayments of principal</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Collections of Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateCollectionsOfPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:to="lab_srt_MortgageLoansOnRealEstateCollectionsOfPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_5664ca7f-3443-4486-871c-c5d902e2d905_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_c6077d45-c56b-4172-85be-edff3ab4932c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward_a14f1a84-0adc-409a-b4c4-10e3d8fd5064_verboseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Operating Real Estate</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward" xlink:to="lab_us-gaap_ReconciliationOfCarryingAmountOfRealEstateInvestmentsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_2b8f922f-fc46-4528-a543-cfeb26b157bd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_3b8d6e94-b235-4b78-a81f-0af2ec4951de_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemptions of redeemable non-controlling interest in Consolidated VIE</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Redeemable Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfRedeemableNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_OperatingRealEstateNet_1800e9a8-2119-49a1-b6e6-8b9eabe2f334_terseLabel_en-US" xlink:label="lab_adam_OperatingRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate, net</link:label>
    <link:label id="lab_adam_OperatingRealEstateNet_label_en-US" xlink:label="lab_adam_OperatingRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Real Estate, Net</link:label>
    <link:label id="lab_adam_OperatingRealEstateNet_documentation_en-US" xlink:label="lab_adam_OperatingRealEstateNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Real Estate, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OperatingRealEstateNet" xlink:href="adam-20251231.xsd#adam_OperatingRealEstateNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_OperatingRealEstateNet" xlink:to="lab_adam_OperatingRealEstateNet" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_A9.250SeniorNotesDue2031Member_019c2214-501a-7e51-81c8-e6123a67a2ff_terseLabel_en-US" xlink:label="lab_adam_A9.250SeniorNotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">9.250% Senior Notes due 2031</link:label>
    <link:label id="lab_adam_A9.250SeniorNotesDue2031Member_label_en-US" xlink:label="lab_adam_A9.250SeniorNotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">9.250% Senior Notes due 2031 [Member]</link:label>
    <link:label id="lab_adam_A9.250SeniorNotesDue2031Member_documentation_en-US" xlink:label="lab_adam_A9.250SeniorNotesDue2031Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">9.250% Senior Notes due 2031</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A9.250SeniorNotesDue2031Member" xlink:href="adam-20251231.xsd#adam_A9.250SeniorNotesDue2031Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_A9.250SeniorNotesDue2031Member" xlink:to="lab_adam_A9.250SeniorNotesDue2031Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_3bcf9841-e19f-4bee-bf4b-3c95343a88bc_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_c733abcb-224b-4ea8-af70-f98004ae4547_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList_ad572e0a-473d-4518-a3df-cd060547a415_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues"/>
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    <link:label id="lab_us-gaap_SecuredDebtMember_e645ccc8-c598-4940-ba25-ed775e480383_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured debt</link:label>
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    <link:label id="lab_us-gaap_LongTermDebt_06d0a1a0-48b2-487b-9a56-5cda6bf45d87_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_b009e89c-ed60-4ccd-9d72-28f86f570bc6_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_c2341918-6c00-4534-8e34-0695757a919d_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate, carrying value</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock_c95bfb34-18ea-475a-b936-72205a92bad8_terseLabel_en-US" xlink:label="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:label id="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights, Policy [Policy Text Block]</link:label>
    <link:label id="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:href="adam-20251231.xsd#adam_MortgageServicingRightsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:to="lab_adam_MortgageServicingRightsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_3cf64c95-61d4-4e02-bef2-bed71dd028d1_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_4ed577fc-db03-4726-969a-cfd712525864_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_0722a043-80f6-4be1-9109-16c9dac31ca0_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock_9b85f53e-419a-436a-840a-5ce18a58658c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of RSU Award Activity</link:label>
    <link:label id="lab_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Nonvested Restricted Stock Units Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfNonvestedRestrictedStockUnitsActivityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019bf84d-4f6a-715b-a11d-6aa8aaaf1bb8_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_d2eb198c-3114-4698-a7ac-0b74da3f7c29_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateTable_e818a485-26cb-46fc-887a-d5f202dd0d08_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:label id="lab_us-gaap_RealEstateTable_label_en-US" xlink:label="lab_us-gaap_RealEstateTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateTable" xlink:to="lab_us-gaap_RealEstateTable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PortfolioInvestmentsMember_38509e41-5ff7-4b4f-a7af-33b6a13bfe6e_terseLabel_en-US" xlink:label="lab_adam_PortfolioInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements</link:label>
    <link:label id="lab_adam_PortfolioInvestmentsMember_label_en-US" xlink:label="lab_adam_PortfolioInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portfolio Investments [Member]</link:label>
    <link:label id="lab_adam_PortfolioInvestmentsMember_documentation_en-US" xlink:label="lab_adam_PortfolioInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The type or description of the financial arrangement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PortfolioInvestmentsMember" xlink:href="adam-20251231.xsd#adam_PortfolioInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PortfolioInvestmentsMember" xlink:to="lab_adam_PortfolioInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_858113d7-4d09-4b01-892e-fbe16216a993_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_StPetersburgFLMember_20cf3cec-9c94-4c27-bc97-dc4c04f10bae_terseLabel_en-US" xlink:label="lab_adam_StPetersburgFLMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">St Petersburg, FL</link:label>
    <link:label id="lab_adam_StPetersburgFLMember_label_en-US" xlink:label="lab_adam_StPetersburgFLMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">St. Petersburg, FL [Member]</link:label>
    <link:label id="lab_adam_StPetersburgFLMember_documentation_en-US" xlink:label="lab_adam_StPetersburgFLMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">St. Petersburg, FL</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_StPetersburgFLMember" xlink:href="adam-20251231.xsd#adam_StPetersburgFLMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_StPetersburgFLMember" xlink:to="lab_adam_StPetersburgFLMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_ff8b000b-b924-4ee1-ba20-7c43f37475c9_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingDomain_ba54584f-7f0f-41ba-8382-9ab52ae6cabb_terseLabel_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Domain]</link:label>
    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingDomain_label_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ExternalCreditRatingByGroupingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:to="lab_us-gaap_ExternalCreditRatingByGroupingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_39d5a68f-7b2a-4c88-9200-4588de5fbccb_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows from Operating Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_3668e3c7-901e-4493-a58d-b33ac1ed7a0e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:label id="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis_label_en-US" xlink:label="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:to="lab_us-gaap_AccountsNotesLoansAndFinancingReceivableByReceivableTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_6573ebde-2e2d-4982-ac1d-02f079b18395_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating real estate</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyAtCost_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, at Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyAtCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyAtCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_50f2d657-0997-46db-961c-37d5ba02e1a9_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense_5e2cba70-ee9c-44e5-b756-33157bcd46e9_terseLabel_en-US" xlink:label="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization expense related to operating real estate</link:label>
    <link:label id="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense_d31c6cab-f0d4-448f-a4b2-41ec70ff8eae_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Depreciation</link:label>
    <link:label id="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense_label_en-US" xlink:label="lab_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Accumulated Depreciation, Depreciation Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SECScheduleIIIRealEstateAccumulatedDepreciationDepreciationExpense"/>
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    <link:label id="lab_adam_NumberOfSecuritizationTrusts_4ff72c16-c65f-4efb-9028-2de4ee79bef1_terseLabel_en-US" xlink:label="lab_adam_NumberOfSecuritizationTrusts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securitization trusts</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale_019c2221-ace2-7316-9a03-a7215f2d3ba4_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales and repayments of residential loans held for sale</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Collection, Loan, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndCollectionOfLoansHeldforsale"/>
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    <link:label id="lab_us-gaap_InterestExpenseBorrowings_0cb38e7e-c707-4706-8bf3-cdc6f39916c0_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseBorrowings_label_en-US" xlink:label="lab_us-gaap_InterestExpenseBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseBorrowings" xlink:to="lab_us-gaap_InterestExpenseBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract_4d982a8f-bdd2-40ca-a824-35bc453eaec4_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents and Restricted Cash Reconciliation:</link:label>
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    <link:label id="lab_us-gaap_LongTermNotesPayable_fdb6c52e-fe4f-4eca-ba57-fc843386ef6b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate, net</link:label>
    <link:label id="lab_us-gaap_LongTermNotesPayable_label_en-US" xlink:label="lab_us-gaap_LongTermNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermNotesPayable"/>
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    <link:label id="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements_f7eeabab-ed28-4388-a733-b551a3785d99_terseLabel_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate</link:label>
    <link:label id="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements_label_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty, Weighted Average Interest Rate Of Agreements</link:label>
    <link:label id="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements_documentation_en-US" xlink:label="lab_adam_RepurchaseAgreementCounterpartyWeightedAverageInterestRateOfAgreements" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Agreement Counterparty, Weighted Average Interest Rate Of Agreements</link:label>
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    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_7bc63845-9f67-47eb-a902-37303f81f070_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019bf84d-4f6a-783f-9f96-888260dd0ae2_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
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    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_480bdb8e-af6f-4b4c-b25e-0ccb29c84c28_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_0eac7d9d-4a9d-4362-ad21-124533d07862_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared per common share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_label_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Dividends, Per Share, Declared</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockDividendsPerShareDeclared" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockDividendsPerShareDeclared"/>
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    <link:label id="lab_us-gaap_OtherInvestments_94133014-e9c6-4776-9179-c0a56cde4bd8_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment amount</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_label_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestments" xlink:to="lab_us-gaap_OtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationVariableInterestEntityPolicy_242c5b0d-919b-4d92-94a2-d36a50903135_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation and Variable Interest Entities / Redeemable Non-Controlling Interest in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_ConsolidationVariableInterestEntityPolicy_label_en-US" xlink:label="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Variable Interest Entity, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationVariableInterestEntityPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:to="lab_us-gaap_ConsolidationVariableInterestEntityPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_0de1fbb0-9a27-40b8-98a6-523febd8e0c0_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_97029730-a7d0-4889-af5c-6032fd5f913b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets_019bf84d-4f6a-7c72-ae87-d33c6ddd0117_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total identifiable assets acquired</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_62091707-6199-4aad-80e9-6017c766e43d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_190c3498-d930-45ab-a4dc-cb0aef3a8a2e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local tax provision</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, State and Local Income Taxes, Amount</link:label>
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    <link:label id="lab_us-gaap_EquityMethodInvestments_b541ffe3-d84d-4c59-8d04-050c222f5d8c_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity investments, at fair value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_73578738-9783-4a5e-8cc9-ef57e06ba339_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Equity Investments, carrying value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse_019c680e-2760-7a19-a76e-27b9f52bccd5_terseLabel_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total impairment loss on reclassification to disposal group held for sale</link:label>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse_label_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Reclassified To Held-For-Use</link:label>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse_documentation_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Reclassified To Held-For-Use</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:href="adam-20251231.xsd#adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:to="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUse" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019be5a9-a7d3-7945-8e9b-887377914ed4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_cfe8106b-4e30-4182-a159-3c90dce993ff_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized loss</link:label>
    <link:label id="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal_label_en-US" xlink:label="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Not Discontinued Operation, Gain (Loss) on Disposal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:to="lab_us-gaap_DisposalGroupNotDiscontinuedOperationGainLossOnDisposal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepurchaseAgreementsCollateralPolicy_24f34feb-c4ee-4f99-abf1-b7757f8bc344_terseLabel_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsCollateralPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Residential Loans, Real Estate Owned and Single-family Rental Properties</link:label>
    <link:label id="lab_us-gaap_RepurchaseAgreementsCollateralPolicy_label_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsCollateralPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements, Collateral, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepurchaseAgreementsCollateralPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepurchaseAgreementsCollateralPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepurchaseAgreementsCollateralPolicy" xlink:to="lab_us-gaap_RepurchaseAgreementsCollateralPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_bb0efe0f-1650-4b06-976e-8b0c75238fd1_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019c2856-fbcf-7d23-8eaf-85dd8f855265_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Equity investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_92434697-7f43-4dd9-9baf-d60d03e0deca_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsMember" xlink:to="lab_us-gaap_EquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesSubscriptions_d2b373a6-bed5-47f2-b774-ac8d0d2e933f_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesSubscriptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock subscriptions (up to)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesSubscriptions_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesSubscriptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Subscriptions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesSubscriptions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesSubscriptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesSubscriptions" xlink:to="lab_us-gaap_CommonStockSharesSubscriptions" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SwapMaturities2044Member_1199b299-cd7b-4c49-bf8e-42bbedf57901_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2044Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2044</link:label>
    <link:label id="lab_adam_SwapMaturities2044Member_label_en-US" xlink:label="lab_adam_SwapMaturities2044Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swap Maturities 2044 [Member]</link:label>
    <link:label id="lab_adam_SwapMaturities2044Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2044Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2044</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2044Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2044Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SwapMaturities2044Member" xlink:to="lab_adam_SwapMaturities2044Member" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FixedRatePaymentsMember_890872ac-a160-4fd0-85ff-3ce5d91d8d86_terseLabel_en-US" xlink:label="lab_adam_FixedRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Rate Payments</link:label>
    <link:label id="lab_adam_FixedRatePaymentsMember_label_en-US" xlink:label="lab_adam_FixedRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Rate Payments [Member]</link:label>
    <link:label id="lab_adam_FixedRatePaymentsMember_documentation_en-US" xlink:label="lab_adam_FixedRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Rate Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FixedRatePaymentsMember" xlink:href="adam-20251231.xsd#adam_FixedRatePaymentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FixedRatePaymentsMember" xlink:to="lab_adam_FixedRatePaymentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResidentialMortgageMember_aef112d0-4c39-4c0f-bfb4-dec8b4fc457e_terseLabel_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential Loans</link:label>
    <link:label id="lab_us-gaap_ResidentialMortgageMember_label_en-US" xlink:label="lab_us-gaap_ResidentialMortgageMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResidentialMortgageMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ResidentialMortgageMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResidentialMortgageMember" xlink:to="lab_us-gaap_ResidentialMortgageMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_9edefd9f-0268-4845-9240-4df7d5e51fff_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Income Tax Provision</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock"/>
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    <link:label id="lab_us-gaap_PlanNameAxis_8691fc21-6425-4941-9697-4e0a38459b9d_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1_019c224e-b4d2-75fd-bfb1-5da45b4a89ca_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation of assets acquired in business combination</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Value of Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1"/>
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    <link:label id="lab_dei_DocumentInformationTable_633c1685-6bf2-4373-9587-5d5efd2bd821_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentInformationTable"/>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_713a12e6-f575-4a0e-b326-68b748a3ebef_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfers in</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
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    <link:label id="lab_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet_d8f0c28e-5e9c-41d0-b590-c9399575cce5_terseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family loans, at fair value</link:label>
    <link:label id="lab_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet_7c50b7ec-a8d1-41c0-8b67-8e8636eaed4e_totalLabel_en-US" xlink:label="lab_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total, at Fair Value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet" xlink:href="adam-20251231.xsd#adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet" xlink:to="lab_adam_FinancialInstrumentOwnedLoansAndPreferredEquityNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_6dea0aca-6e2c-47a7-9656-f6ab8a13f9f5_terseLabel_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ancillary and other fee income</link:label>
    <link:label id="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount_label_en-US" xlink:label="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ancillary Fee Income Generated by Servicing Financial Assets, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:to="lab_us-gaap_AncillaryFeeIncomeGeneratedByServicingFinancialAssetsAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities_019bf84d-4f6a-7b3f-ba09-09f65ebb60a5_terseLabel_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements and warehouse facilities</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities_label_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements And Warehouse Facilities</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities_documentation_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Repurchase Agreements And Warehouse Facilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:href="adam-20251231.xsd#adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:to="lab_adam_BusinessCombinationRecognizedLiabilityAssumedRepurchaseAgreementsAndWarehouseFacilities" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_GainLossOnTransferToRealEstateHeldForSale_89f53f31-5351-40cf-b273-00f9c4b6e033_negatedTerseLabel_en-US" xlink:label="lab_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on transfer to real estate held-for-sale</link:label>
    <link:label id="lab_adam_GainLossOnTransferToRealEstateHeldForSale_label_en-US" xlink:label="lab_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Transfer To Real Estate Held-For-Sale</link:label>
    <link:label id="lab_adam_GainLossOnTransferToRealEstateHeldForSale_documentation_en-US" xlink:label="lab_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) On Transfer To Real Estate Held-For-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:href="adam-20251231.xsd#adam_GainLossOnTransferToRealEstateHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:to="lab_adam_GainLossOnTransferToRealEstateHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseMediumTermNotes_5f06187b-f8f7-4561-8d2e-c7a5f8b54b65_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseMediumTermNotes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior unsecured notes</link:label>
    <link:label id="lab_us-gaap_InterestExpenseMediumTermNotes_label_en-US" xlink:label="lab_us-gaap_InterestExpenseMediumTermNotes" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Medium-Term Note</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseMediumTermNotes" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseMediumTermNotes"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseMediumTermNotes" xlink:to="lab_us-gaap_InterestExpenseMediumTermNotes" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageLoansUnder100000Member_ae0a7985-c434-4891-8ec8-cb66322c03d0_terseLabel_en-US" xlink:label="lab_adam_MortgageLoansUnder100000Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Loans Under $100,000</link:label>
    <link:label id="lab_adam_MortgageLoansUnder100000Member_label_en-US" xlink:label="lab_adam_MortgageLoansUnder100000Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans Under $100,000 [Member]</link:label>
    <link:label id="lab_adam_MortgageLoansUnder100000Member_documentation_en-US" xlink:label="lab_adam_MortgageLoansUnder100000Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans Under $100,000</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageLoansUnder100000Member" xlink:href="adam-20251231.xsd#adam_MortgageLoansUnder100000Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MortgageLoansUnder100000Member" xlink:to="lab_adam_MortgageLoansUnder100000Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_26662368-f3c1-4ec1-8c19-5b9b4ebd4c3d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in valuation allowance</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne_df461e19-43a4-4f48-aa7a-502f7dd38ea9_terseLabel_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne_label_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year One</link:label>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne_documentation_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:href="adam-20251231.xsd#adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:to="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearOne" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_07a56571-4959-41f3-818f-a4f6eb125107_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FloatingRatePaymentsMember_ebe8cf03-26fb-4399-a441-0ddef47fc762_terseLabel_en-US" xlink:label="lab_adam_FloatingRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Floating Rate Payments</link:label>
    <link:label id="lab_adam_FloatingRatePaymentsMember_label_en-US" xlink:label="lab_adam_FloatingRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Floating Rate Payments [Member]</link:label>
    <link:label id="lab_adam_FloatingRatePaymentsMember_documentation_en-US" xlink:label="lab_adam_FloatingRatePaymentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Floating Rate Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FloatingRatePaymentsMember" xlink:href="adam-20251231.xsd#adam_FloatingRatePaymentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FloatingRatePaymentsMember" xlink:to="lab_adam_FloatingRatePaymentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset_019bf84d-4f6a-72dc-8162-c38903e0a76e_terseLabel_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset_label_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Other Asset</link:label>
    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset_documentation_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Other Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:href="adam-20251231.xsd#adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:to="lab_adam_BusinessCombinationRecognizedAssetAcquiredOtherAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SecuredDebtFairValue_f332e221-be85-4813-ad92-043dd3fee2a1_verboseLabel_en-US" xlink:label="lab_adam_SecuredDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations, fair value</link:label>
    <link:label id="lab_adam_SecuredDebtFairValue_label_en-US" xlink:label="lab_adam_SecuredDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt Fair Value</link:label>
    <link:label id="lab_adam_SecuredDebtFairValue_documentation_en-US" xlink:label="lab_adam_SecuredDebtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair value of secured debt.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SecuredDebtFairValue" xlink:href="adam-20251231.xsd#adam_SecuredDebtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SecuredDebtFairValue" xlink:to="lab_adam_SecuredDebtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_5db1756f-aee3-46c7-943e-4790b55c9f59_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement [Abstract]</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_dbecbb20-2115-4ea7-adea-ee111d367999_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents and Restricted Cash - Beginning of Period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_8c6363f5-24cd-4377-a909-ecb528855616_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents and Restricted Cash - End of Period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_bc4dcbb6-0871-481a-8ff4-073da7c2b7ff_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total cash, cash equivalents, and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_5c8db760-dc3d-4da9-9096-c23a93c82294_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssets_e846e325-a43d-4f1e-923c-cec62ac5f392_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_f949dac5-4507-424c-b7bc-090a1e7602b9_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Derivative asset, carrying value</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareCashPaid_ae5c17e2-a5fc-490d-ae8b-eaf95bc454c3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash dividend per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsPerShareCashPaid_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockDividendsPerShareCashPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:to="lab_us-gaap_PreferredStockDividendsPerShareCashPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialMortgageLoansAtFairValueMember_a045c62c-2502-4ada-a3d4-f27a465fd62c_verboseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans</link:label>
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    <link:label id="lab_adam_ResidentialMortgageLoansAtFairValueMember_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans At Fair Value [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansAtFairValueMember" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansAtFairValueMember"/>
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    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_6e9f9d9d-4ece-4e12-9065-290ba237b5b1_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoninterestIncomeOther_07d52f19-dc73-4f27-a4a1-e751dda72534_terseLabel_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_NoninterestIncomeOther_label_en-US" xlink:label="lab_us-gaap_NoninterestIncomeOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noninterest Income, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoninterestIncomeOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoninterestIncomeOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoninterestIncomeOther" xlink:to="lab_us-gaap_NoninterestIncomeOther" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_64c30520-7522-47a7-8d98-6166b5a8fe40_terseLabel_en-US" xlink:label="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">8.000% Series D Fixed-to-Floating Rate Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
    <link:label id="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_label_en-US" xlink:label="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">8.000% Series D Fixed-to-Floating Rate Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference [Member]</link:label>
    <link:label id="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember_documentation_en-US" xlink:label="lab_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">8.000% Series D Fixed-to-Floating Rate Cumulative Redeemable Preferred Stock, par value $0.01 per share, $25.00 Liquidation Preference</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember" xlink:href="adam-20251231.xsd#adam_A8000SeriesDFixedToFloatingRateCumulativeRedeemablePreferredStockParValue001PerShare2500LiquidationPreferenceMember"/>
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    <link:label id="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfMortgagesPayableOnRealEstateHeld_61b4d4cf-00f2-45f3-a8ca-e2532bb9e6da_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashDispositionDeConsolidationOfMortgagesPayableOnRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">De-consolidation of mortgages payable on real estate held in Consolidated VIEs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_NoncashOrPartNoncashDispositionDeConsolidationOfMortgagesPayableOnRealEstateHeld" xlink:href="adam-20251231.xsd#adam_NoncashOrPartNoncashDispositionDeConsolidationOfMortgagesPayableOnRealEstateHeld"/>
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    <link:label id="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue_0a14123c-04f3-4a46-9732-e88098584ce5_terseLabel_en-US" xlink:label="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, available for future issuance</link:label>
    <link:label id="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue_label_en-US" xlink:label="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Reserved For Future Issuance, Value</link:label>
    <link:label id="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue_documentation_en-US" xlink:label="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Reserved For Future Issuance, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:href="adam-20251231.xsd#adam_PreferredStockSharesReservedForFutureIssuanceValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:to="lab_adam_PreferredStockSharesReservedForFutureIssuanceValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_f6ae2ba6-69bb-4533-817b-f4cbc658de80_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss)</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_9be62a57-0f46-4c29-8445-632089c8f4be_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Company Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019bf84d-4f6a-7df3-ad4c-e310551b2492_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_2b37e6ab-fba7-40ff-8887-88f202c15212_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_LiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_d086741b-c3f0-4cc0-97e9-4a129747844c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_bb01f882-4379-4332-b726-d4493d951ca5_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome_5ce08354-d43a-45e4-9f30-98d76c861cc5_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Non-taxable REIT (income) loss</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Exempt Income, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxExemptIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxExemptIncome"/>
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    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_019bf84d-4f6a-7b81-8c55-d9d90e825c37_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of the Estimated Fair Values of the Assets Acquired and Liabilities Assumed by the Company at the Acquisition Date</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_OtherRealEstate_92d271cc-f743-4f80-a0e5-64a03e3ffea1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets in consolidated multi-family properties</link:label>
    <link:label id="lab_us-gaap_OtherRealEstate_label_en-US" xlink:label="lab_us-gaap_OtherRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherRealEstate" xlink:to="lab_us-gaap_OtherRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MeasurementInputAnnualHomePriceAppreciationMember_b76b9ff1-9b9f-4a27-95e8-d5b4c4104b09_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputAnnualHomePriceAppreciationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Annual home price appreciation/(depreciation)</link:label>
    <link:label id="lab_adam_MeasurementInputAnnualHomePriceAppreciationMember_label_en-US" xlink:label="lab_adam_MeasurementInputAnnualHomePriceAppreciationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Annual Home Price Appreciation [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputAnnualHomePriceAppreciationMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputAnnualHomePriceAppreciationMember"/>
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    <link:label id="lab_dei_CityAreaCode_203c0d6a-6006-4d50-917b-64a3c3afd7e1_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CommodityFuturesMember_019c4220-440f-7b09-bb7d-616d2b4bfbd6_terseLabel_en-US" xlink:label="lab_adam_CommodityFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commodity futures</link:label>
    <link:label id="lab_adam_CommodityFuturesMember_label_en-US" xlink:label="lab_adam_CommodityFuturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commodity Futures [Member]</link:label>
    <link:label id="lab_adam_CommodityFuturesMember_documentation_en-US" xlink:label="lab_adam_CommodityFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commodity Futures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CommodityFuturesMember" xlink:href="adam-20251231.xsd#adam_CommodityFuturesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CommodityFuturesMember" xlink:to="lab_adam_CommodityFuturesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract_019c2ea5-1f9d-7c49-8293-d1b5a90bca88_terseLabel_en-US" xlink:label="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GAAP/Tax differences</link:label>
    <link:label id="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract_label_en-US" xlink:label="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, GAAP/Tax basis differences [Abstract]</link:label>
    <link:label id="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract_documentation_en-US" xlink:label="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, GAAP/Tax basis differences</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:href="adam-20251231.xsd#adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:to="lab_adam_DeferredTaxAssetsGAAPTaxBasisDifferencesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MortgagesMember_34578f79-8834-418e-9166-b94bcf99cbc8_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate</link:label>
    <link:label id="lab_us-gaap_MortgagesMember_label_en-US" xlink:label="lab_us-gaap_MortgagesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgages [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgagesMember" xlink:to="lab_us-gaap_MortgagesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_dd83b4a8-2b7d-482b-8d99-f9bf985e942a_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Paydowns</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged_b0ad2ac1-b1b3-4f50-a00f-04521af4b1cd_terseLabel_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost of Collateral Pledged</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged_label_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold Under Agreements To Repurchase, Amortized Cost Of Collateral Pledged</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged_documentation_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Sold Under Agreements To Repurchase, Amortized Cost Of Collateral Pledged</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:href="adam-20251231.xsd#adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:to="lab_adam_AssetsSoldUnderAgreementsToRepurchaseAmortizedCostOfCollateralPledged" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariationMarginReceivableDerivative_4565b31d-7335-4e19-b2c6-3b8bdd37e600_verboseLabel_en-US" xlink:label="lab_us-gaap_VariationMarginReceivableDerivative" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Variation Margin</link:label>
    <link:label id="lab_us-gaap_VariationMarginReceivableDerivative_827c0d13-1b41-4c81-adca-d69cd5a8237e_terseLabel_en-US" xlink:label="lab_us-gaap_VariationMarginReceivableDerivative" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variation Margin</link:label>
    <link:label id="lab_us-gaap_VariationMarginReceivableDerivative_label_en-US" xlink:label="lab_us-gaap_VariationMarginReceivableDerivative" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variation Margin Receivable, Derivative</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariationMarginReceivableDerivative" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariationMarginReceivableDerivative"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariationMarginReceivableDerivative" xlink:to="lab_us-gaap_VariationMarginReceivableDerivative" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_8184c818-5c12-4e22-98fe-a7f7f9a54998_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows from Investing Activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_780e8aff-ba88-46c9-908f-5bceb9685936_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_InterestExpenseRealEstateMortgagePayable_b0f4c61b-028f-4ee2-82db-90d7f35cfe49_terseLabel_en-US" xlink:label="lab_adam_InterestExpenseRealEstateMortgagePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense, mortgages payable on real estate</link:label>
    <link:label id="lab_adam_InterestExpenseRealEstateMortgagePayable_label_en-US" xlink:label="lab_adam_InterestExpenseRealEstateMortgagePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Real Estate Mortgage Payable</link:label>
    <link:label id="lab_adam_InterestExpenseRealEstateMortgagePayable_documentation_en-US" xlink:label="lab_adam_InterestExpenseRealEstateMortgagePayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Expense, Real Estate Mortgage Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_InterestExpenseRealEstateMortgagePayable" xlink:href="adam-20251231.xsd#adam_InterestExpenseRealEstateMortgagePayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_InterestExpenseRealEstateMortgagePayable" xlink:to="lab_adam_InterestExpenseRealEstateMortgagePayable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_OtherRealEstateIncome_162c8ef6-6ebd-4f10-b2d3-02f32b5abc3a_terseLabel_en-US" xlink:label="lab_adam_OtherRealEstateIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other real estate income</link:label>
    <link:label id="lab_adam_OtherRealEstateIncome_label_en-US" xlink:label="lab_adam_OtherRealEstateIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate Income</link:label>
    <link:label id="lab_adam_OtherRealEstateIncome_documentation_en-US" xlink:label="lab_adam_OtherRealEstateIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Real Estate Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OtherRealEstateIncome" xlink:href="adam-20251231.xsd#adam_OtherRealEstateIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_OtherRealEstateIncome" xlink:to="lab_adam_OtherRealEstateIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MarginDepositAssetsInitialAmount_75655f1f-754d-4fc0-a07d-46122a04a5ce_terseLabel_en-US" xlink:label="lab_adam_MarginDepositAssetsInitialAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Margin deposit assets, initial amount</link:label>
    <link:label id="lab_adam_MarginDepositAssetsInitialAmount_label_en-US" xlink:label="lab_adam_MarginDepositAssetsInitialAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Margin Deposit Assets, Initial Amount</link:label>
    <link:label id="lab_adam_MarginDepositAssetsInitialAmount_documentation_en-US" xlink:label="lab_adam_MarginDepositAssetsInitialAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Margin Deposit Assets, Initial Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MarginDepositAssetsInitialAmount" xlink:href="adam-20251231.xsd#adam_MarginDepositAssetsInitialAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MarginDepositAssetsInitialAmount" xlink:to="lab_adam_MarginDepositAssetsInitialAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ComponentsOfServicingRevenueTableTextBlock_db608c3f-92f0-4ab3-a0c3-1ae8d9dcd228_terseLabel_en-US" xlink:label="lab_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Servicing Income</link:label>
    <link:label id="lab_adam_ComponentsOfServicingRevenueTableTextBlock_label_en-US" xlink:label="lab_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Components of Servicing Revenue [Table Text Block]</link:label>
    <link:label id="lab_adam_ComponentsOfServicingRevenueTableTextBlock_documentation_en-US" xlink:label="lab_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Components of Servicing Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:href="adam-20251231.xsd#adam_ComponentsOfServicingRevenueTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:to="lab_adam_ComponentsOfServicingRevenueTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_6f03e2cb-2592-41e6-b5ff-1aed542bc84d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_fb0ef3d8-8b1f-40b4-97b6-bec78407f361_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut_0eb348da-4b43-448a-b9f9-868d1cafb8b9_negatedLabel_en-US" xlink:label="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Terminations/Transfers Out</link:label>
    <link:label id="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut_label_en-US" xlink:label="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notional Amount Of Other Derivatives, Terminations, Transfers Out</link:label>
    <link:label id="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut_documentation_en-US" xlink:label="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Settlement, expiration, or exercise for notional amount of other derivatives.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:href="adam-20251231.xsd#adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:to="lab_adam_NotionalAmountOfOtherDerivativesTerminationsTransfersOut" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_1eee5b30-1a3e-46d1-ad90-99f409217a1b_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, Disposed of by Sale, Not Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember_label_en-US" xlink:label="lab_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Disposed of by Sale, Not Discontinued Operations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:to="lab_us-gaap_DisposalGroupDisposedOfBySaleNotDiscontinuedOperationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsMember_019b06fa-a5ba-71ed-9930-609d1169e871_verboseLabel_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations, at amortized cost, net</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsMember_91e07301-c640-44bd-83bd-d650297e2690_terseLabel_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations at amortized cost, net</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsMember_label_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Collateralized Debt Obligations [Member]</link:label>
    <link:label id="lab_adam_ResidentialCollateralizedDebtObligationsMember_documentation_en-US" xlink:label="lab_adam_ResidentialCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential collateralized debt obligations.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialCollateralizedDebtObligationsMember" xlink:href="adam-20251231.xsd#adam_ResidentialCollateralizedDebtObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialCollateralizedDebtObligationsMember" xlink:to="lab_adam_ResidentialCollateralizedDebtObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilities_3e8508c6-6189-4f47-bbfc-d056e854cc64_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_d590b494-5fcd-4bf7-8271-784149ab3021_totalLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_OtherLiabilities_label_en-US" xlink:label="lab_us-gaap_OtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilities" xlink:to="lab_us-gaap_OtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019b8cb9-fb54-7110-8b38-36d032dbcee7_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMeasurementInput_f5325e94-8f89-458d-84ef-a7c29e4df625_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt, measurement input</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMeasurementInput_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMeasurementInput" xlink:to="lab_us-gaap_LongTermDebtMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_TotalCollateralizedDebtObligationsMember_b5c33552-aa9a-4c84-8351-8f007e0c0f51_terseLabel_en-US" xlink:label="lab_adam_TotalCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total collateralized debt obligations</link:label>
    <link:label id="lab_adam_TotalCollateralizedDebtObligationsMember_label_en-US" xlink:label="lab_adam_TotalCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Collateralized Debt Obligations [Member]</link:label>
    <link:label id="lab_adam_TotalCollateralizedDebtObligationsMember_documentation_en-US" xlink:label="lab_adam_TotalCollateralizedDebtObligationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total Collateralized Debt Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_TotalCollateralizedDebtObligationsMember" xlink:href="adam-20251231.xsd#adam_TotalCollateralizedDebtObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_TotalCollateralizedDebtObligationsMember" xlink:to="lab_adam_TotalCollateralizedDebtObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans_b2b2b1f8-c45b-487f-99fe-5298236eb1cb_terseLabel_en-US" xlink:label="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments to fund advances for business purpose loans</link:label>
    <link:label id="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans_label_en-US" xlink:label="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecorded Commitment To Fund Advances On Business Purpose Loans</link:label>
    <link:label id="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans_documentation_en-US" xlink:label="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrecorded Commitment To Fund Advances On Business Purpose Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:href="adam-20251231.xsd#adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:to="lab_adam_UnrecordedCommitmentToFundAdvancesOnBusinessPurposeLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetInterestCarryforward_019c4172-7ab7-7702-8721-a30b85bb69dc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense limitation carryforward</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetInterestCarryforward_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Interest Carryforward</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetInterestCarryforward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:to="lab_us-gaap_DeferredTaxAssetInterestCarryforward" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NumberOfJointVenturesImpairedDuringPeriod_019be4ba-c253-7301-8a6c-22ae09cbbb42_terseLabel_en-US" xlink:label="lab_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of joint ventures impaired during period</link:label>
    <link:label id="lab_adam_NumberOfJointVenturesImpairedDuringPeriod_label_en-US" xlink:label="lab_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Joint Ventures Impaired During Period</link:label>
    <link:label id="lab_adam_NumberOfJointVenturesImpairedDuringPeriod_documentation_en-US" xlink:label="lab_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Joint Ventures Impaired During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:href="adam-20251231.xsd#adam_NumberOfJointVenturesImpairedDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:to="lab_adam_NumberOfJointVenturesImpairedDuringPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_9660e958-a496-467a-8490-e0b61f51d8b8_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_9ce57f58-6a07-43aa-bd35-53890b251c97_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfers out</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers out of Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans_019c414f-a4a0-7774-aa93-f99d597a339e_negatedTerseLabel_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Transfer from residential loans held for sale to residential loans</link:label>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans_label_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers From Residential Loans Held For Sale to Residential Loans</link:label>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans_documentation_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers From Residential Loans Held For Sale to Residential Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:href="adam-20251231.xsd#adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:to="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersFromResidentialLoansHeldForSaleToResidentialLoans" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_0f6f7471-6265-456e-a516-56b59950a971_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock_5ca903a2-cd57-4042-81a0-afcca1a07450_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Unencumbered Securities</link:label>
    <link:label id="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock_label_en-US" xlink:label="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Unencumbered Securities [Table Text Block]</link:label>
    <link:label id="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock_documentation_en-US" xlink:label="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Unencumbered Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfUnencumberedSecuritiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:to="lab_adam_ScheduleOfUnencumberedSecuritiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_f967c842-472c-4690-a1b4-4d7980882efb_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_db137e82-6881-4995-b0a4-5fa02ba958f8_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage Servicing Rights</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing of Financial Assets [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:to="lab_us-gaap_TransfersAndServicingOfFinancialAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_e11979d8-fbf7-4eeb-9d62-c3a827c39dc3_terseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gains on sales of investment real estate</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gains (Losses) on Sales of Investment Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainsLossesOnSalesOfInvestmentRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:to="lab_us-gaap_GainsLossesOnSalesOfInvestmentRealEstate" xlink:type="arc" order="1"/>
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    <link:label id="lab_adam_SeniorUnsecuredNotesAtFairValueMember_label_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes, At Fair Value [Member]</link:label>
    <link:label id="lab_adam_SeniorUnsecuredNotesAtFairValueMember_documentation_en-US" xlink:label="lab_adam_SeniorUnsecuredNotesAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Unsecured Notes, At Fair Value</link:label>
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    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_487c8ab2-45a3-4498-a894-7dacc8fad52b_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental Disclosure:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_5df019e0-2d89-4ca0-83ad-d975d7d75e94_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Amortized Cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
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    <link:label id="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember_019c4dfe-ea6a-7355-bdf9-82629ed2287c_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group, One Multi-Family Apartment Community</link:label>
    <link:label id="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember_label_en-US" xlink:label="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, One Multi-Family Apartment Community [Member]</link:label>
    <link:label id="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember_documentation_en-US" xlink:label="lab_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, One Multi-Family Apartment Community</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupOneMultiFamilyApartmentCommunityMember" xlink:href="adam-20251231.xsd#adam_DisposalGroupOneMultiFamilyApartmentCommunityMember"/>
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    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RealEstateFederalIncomeTaxBasis_7a799908-3308-422a-b5ef-455c420a3291_terseLabel_en-US" xlink:label="lab_srt_RealEstateFederalIncomeTaxBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of consolidated real estate for federal income tax purposes</link:label>
    <link:label id="lab_srt_RealEstateFederalIncomeTaxBasis_label_en-US" xlink:label="lab_srt_RealEstateFederalIncomeTaxBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Federal Income Tax Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RealEstateFederalIncomeTaxBasis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RealEstateFederalIncomeTaxBasis"/>
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    <link:label id="lab_us-gaap_MarketableSecuritiesPolicy_e4992fb6-f97b-45fe-9154-4546af3eff09_terseLabel_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities Available for Sale</link:label>
    <link:label id="lab_us-gaap_MarketableSecuritiesPolicy_label_en-US" xlink:label="lab_us-gaap_MarketableSecuritiesPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MarketableSecuritiesPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MarketableSecuritiesPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MarketableSecuritiesPolicy" xlink:to="lab_us-gaap_MarketableSecuritiesPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RealEstateOwned_0a21fbfb-6e6b-47f2-9e65-2d8307cb9bdd_terseLabel_en-US" xlink:label="lab_adam_RealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate owned</link:label>
    <link:label id="lab_adam_RealEstateOwned_label_en-US" xlink:label="lab_adam_RealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:label id="lab_adam_RealEstateOwned_documentation_en-US" xlink:label="lab_adam_RealEstateOwned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateOwned" xlink:href="adam-20251231.xsd#adam_RealEstateOwned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RealEstateOwned" xlink:to="lab_adam_RealEstateOwned" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NonAgencyRMBSMember_b9042d2e-c226-45ec-ac19-18ae6416b1b2_terseLabel_en-US" xlink:label="lab_adam_NonAgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Agency RMBS</link:label>
    <link:label id="lab_adam_NonAgencyRMBSMember_label_en-US" xlink:label="lab_adam_NonAgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non Agency RMBS [Member]</link:label>
    <link:label id="lab_adam_NonAgencyRMBSMember_documentation_en-US" xlink:label="lab_adam_NonAgencyRMBSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-agency RMBS.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NonAgencyRMBSMember" xlink:href="adam-20251231.xsd#adam_NonAgencyRMBSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NonAgencyRMBSMember" xlink:to="lab_adam_NonAgencyRMBSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoansAndRealEstateOwnedMember_1939bc44-fe3d-4528-bb38-a4a190c66275_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansAndRealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans and real estate owned</link:label>
    <link:label id="lab_adam_ResidentialLoansAndRealEstateOwnedMember_label_en-US" xlink:label="lab_adam_ResidentialLoansAndRealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loans and Real Estate Owned [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoansAndRealEstateOwnedMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoansAndRealEstateOwnedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans and Real Estate Owned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansAndRealEstateOwnedMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoansAndRealEstateOwnedMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredIncludingEquityInterestInAcquireeHeldPriorToCombination1_019bf84d-4f6a-71b9-a5c1-452edb849fc6_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredIncludingEquityInterestInAcquireeHeldPriorToCombination1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total consideration transferred</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_b41e391d-771e-4785-99d1-8a524029c36a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
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    <link:label id="lab_us-gaap_RestrictedCash_ea78fa0a-3acc-4c04-b43f-909bd47d8445_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCash_label_en-US" xlink:label="lab_us-gaap_RestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCash" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCash"/>
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    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_c353a398-34fb-40e8-bfb7-3f527f08794d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
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    <link:label id="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract_b8b43ce4-745a-4af3-a98c-d76f2b85e94c_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Liabilities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentsFinancialLiabilitiesBalanceSheetGroupingsAbstract"/>
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    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock_ccfb36b1-25aa-4db6-a1c4-a8f5fa090cf6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchases of preferred stock</link:label>
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    <link:label id="lab_adam_TidesOn27thInvestorsLLCMember_894c6b21-6be0-46bd-a421-2c5cf73693a0_terseLabel_en-US" xlink:label="lab_adam_TidesOn27thInvestorsLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tides on 27th Investors, LLC</link:label>
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    <link:label id="lab_adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments In Disposal Group Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember" xlink:to="lab_adam_EquityMethodInvestmentsInDisposalGroupHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_179f750e-a4a9-4414-8228-734c57a4dcbe_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoanSecuritizationMember_081ae1ba-5f75-40ef-a2d5-7d9cfe2bc430_verboseLabel_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations</link:label>
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    <link:label id="lab_adam_ResidentialLoanSecuritizationMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loan Securitization [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoanSecuritizationMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoanSecuritizationMember"/>
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    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_82e5b899-d966-4805-b82e-c76f514f5ce5_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
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    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_e2928cf2-2ad5-497b-8404-9803734d2d88_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasury securities</link:label>
    <link:label id="lab_us-gaap_USTreasurySecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasurySecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Securities [Member]</link:label>
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    <link:label id="lab_adam_StepUpInterestRateTwoMember_03f20787-e03d-49c1-b568-00ea7cbf9693_terseLabel_en-US" xlink:label="lab_adam_StepUpInterestRateTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate Two</link:label>
    <link:label id="lab_adam_StepUpInterestRateTwoMember_label_en-US" xlink:label="lab_adam_StepUpInterestRateTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate Two [Member]</link:label>
    <link:label id="lab_adam_StepUpInterestRateTwoMember_documentation_en-US" xlink:label="lab_adam_StepUpInterestRateTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_StepUpInterestRateTwoMember" xlink:href="adam-20251231.xsd#adam_StepUpInterestRateTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_StepUpInterestRateTwoMember" xlink:to="lab_adam_StepUpInterestRateTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_40dee39c-d494-4fa8-a120-fec82b9055a8_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_CurrentFederalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Federal Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentFederalTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentFederalTaxExpenseBenefit"/>
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    <link:label id="lab_adam_SubservicingFeeExpenses_9b183620-f357-4166-a166-0d165748d9da_terseLabel_en-US" xlink:label="lab_adam_SubservicingFeeExpenses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subservicing fee expenses</link:label>
    <link:label id="lab_adam_SubservicingFeeExpenses_label_en-US" xlink:label="lab_adam_SubservicingFeeExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subservicing Fee Expenses</link:label>
    <link:label id="lab_adam_SubservicingFeeExpenses_documentation_en-US" xlink:label="lab_adam_SubservicingFeeExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Subservicing Fee Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SubservicingFeeExpenses" xlink:href="adam-20251231.xsd#adam_SubservicingFeeExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SubservicingFeeExpenses" xlink:to="lab_adam_SubservicingFeeExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PreferredEquityOwnershipInterestsMember_c6c4b029-7142-4976-bdda-4918310011d6_terseLabel_en-US" xlink:label="lab_adam_PreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Equity Ownership Interests</link:label>
    <link:label id="lab_adam_PreferredEquityOwnershipInterestsMember_label_en-US" xlink:label="lab_adam_PreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Equity Ownership Interests [Member]</link:label>
    <link:label id="lab_adam_PreferredEquityOwnershipInterestsMember_documentation_en-US" xlink:label="lab_adam_PreferredEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Equity Ownership Interests [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredEquityOwnershipInterestsMember" xlink:href="adam-20251231.xsd#adam_PreferredEquityOwnershipInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PreferredEquityOwnershipInterestsMember" xlink:to="lab_adam_PreferredEquityOwnershipInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_GinnieMaeMember_ac68aec4-4392-4e35-b9c0-ea84f7949d3c_terseLabel_en-US" xlink:label="lab_adam_GinnieMaeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ginnie Mae</link:label>
    <link:label id="lab_adam_GinnieMaeMember_label_en-US" xlink:label="lab_adam_GinnieMaeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ginnie Mae [Member]</link:label>
    <link:label id="lab_adam_GinnieMaeMember_documentation_en-US" xlink:label="lab_adam_GinnieMaeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Ginnie Mae</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_GinnieMaeMember" xlink:href="adam-20251231.xsd#adam_GinnieMaeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_GinnieMaeMember" xlink:to="lab_adam_GinnieMaeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_50d5127c-8f13-41e9-913d-3a54e6883cdb_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_019bf84d-4f6a-7136-8cc5-8a6837fc5e00_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
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    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive_09fcbfdf-64fa-4b28-a831-1e74eff77021_terseLabel_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive_label_en-US" xlink:label="lab_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Expected Depreciation, Year Five</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive" xlink:href="adam-20251231.xsd#adam_RealEstateInvestmentPropertyExpectedDepreciationYearFive"/>
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    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_019b8cb7-80fa-74d5-bd1d-699e51a34c4c_terseLabel_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held for sale, at fair value</link:label>
    <link:label id="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Mortgage, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgagesHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgagesHeldForSaleFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansReceivable_11fc0e0f-09a1-442d-b405-2113dbaa2199_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of residential loans</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfLoansReceivable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfLoansReceivable"/>
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    <link:label id="lab_us-gaap_DeconsolidationGainOrLossWithRelatedDisclosuresAbstract_019c656a-c466-72a2-82bb-4e28d4361f62_terseLabel_en-US" xlink:label="lab_us-gaap_DeconsolidationGainOrLossWithRelatedDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sales of the Company's ownership interests in joint venture equity investments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeconsolidationGainOrLossWithRelatedDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeconsolidationGainOrLossWithRelatedDisclosuresAbstract"/>
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    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_9012f54e-5ba3-4693-ae18-e552d5423333_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationDepletionAndAmortization_019b0799-cc92-7cc2-add8-60874819d29d_totalLabel_en-US" xlink:label="lab_us-gaap_DepreciationDepletionAndAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total depreciation and amortization</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationDepletionAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationDepletionAndAmortization"/>
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    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock_b3259656-54cf-4341-bc31-bf9aea61d35c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Preferred Stock Issued and Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Stockholders Equity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockholdersEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockholdersEquityTableTextBlock"/>
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    <link:label id="lab_adam_MeasurementInputPullThroughRateMember_019c2856-fbcf-71bd-b3a5-ce29d6985bbe_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputPullThroughRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pull-through rate</link:label>
    <link:label id="lab_adam_MeasurementInputPullThroughRateMember_label_en-US" xlink:label="lab_adam_MeasurementInputPullThroughRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Pull-Through Rate [Member]</link:label>
    <link:label id="lab_adam_MeasurementInputPullThroughRateMember_documentation_en-US" xlink:label="lab_adam_MeasurementInputPullThroughRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Pull-Through Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputPullThroughRateMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputPullThroughRateMember"/>
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    <link:label id="lab_adam_U.S.TreasuryFuturesMember_019c420f-fe0c-7969-b3bb-4a602adbcb4c_terseLabel_en-US" xlink:label="lab_adam_U.S.TreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. Treasury futures</link:label>
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    <link:label id="lab_adam_U.S.TreasuryFuturesMember_documentation_en-US" xlink:label="lab_adam_U.S.TreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">U.S. Treasury Futures</link:label>
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    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_81d852c4-510e-462a-9bc1-551eb623df83_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases</link:label>
    <link:label id="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans_label_en-US" xlink:label="lab_us-gaap_MortgageLoansOnRealEstateNewMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, New Mortgage Loan</link:label>
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    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
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    <link:label id="lab_adam_StepUpInterestRateThreeMember_documentation_en-US" xlink:label="lab_adam_StepUpInterestRateThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Step-Up Interest Rate Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_StepUpInterestRateThreeMember" xlink:href="adam-20251231.xsd#adam_StepUpInterestRateThreeMember"/>
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    <link:label id="lab_dei_LocalPhoneNumber_3d4cf0a3-979f-4867-93af-4f0000e03305_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
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    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_fa931eb3-d31b-434a-858e-0f0e99d1626d_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_21cde66c-e559-43cc-8363-a3d593ad2442_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
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    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_019c4e32-c6ed-7e56-8f3e-aee982d14138_terseLabel_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased (in shares)</link:label>
    <link:label id="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares_label_en-US" xlink:label="lab_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Repurchased and Retired During Period, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockRepurchasedAndRetiredDuringPeriodShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockRepurchasedAndRetiredDuringPeriodShares"/>
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    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_8ed7f742-0316-469c-85a3-76d4e950668b_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series F Preferred Stock</link:label>
    <link:label id="lab_us-gaap_SeriesFPreferredStockMember_label_en-US" xlink:label="lab_us-gaap_SeriesFPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Series F Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeriesFPreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeriesFPreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeriesFPreferredStockMember" xlink:to="lab_us-gaap_SeriesFPreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed_084454a4-ef52-47dc-a179-270100d7b1be_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification to held and used</link:label>
    <link:label id="lab_adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed_label_en-US" xlink:label="lab_adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Reclassification To Held And Used</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed" xlink:href="adam-20251231.xsd#adam_SECSchedule1228RealEstateCompaniesInvestmentInRealEstateReclassificationToHeldAndUsed"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_019bf84d-4f6a-7923-9d10-352c19769641_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
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    <link:label id="lab_us-gaap_MaturityUpTo30DaysMember_0049bd12-0d15-4780-8c46-13fb90189e09_terseLabel_en-US" xlink:label="lab_us-gaap_MaturityUpTo30DaysMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Within 30 days</link:label>
    <link:label id="lab_us-gaap_MaturityUpTo30DaysMember_label_en-US" xlink:label="lab_us-gaap_MaturityUpTo30DaysMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maturity Less than 30 Days [Member]</link:label>
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    <link:label id="lab_adam_AgencyFixedRateMember_dea49358-7c9f-4884-a5db-5f528e6b6d70_terseLabel_en-US" xlink:label="lab_adam_AgencyFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed rate</link:label>
    <link:label id="lab_adam_AgencyFixedRateMember_label_en-US" xlink:label="lab_adam_AgencyFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency Fixed Rate [Member]</link:label>
    <link:label id="lab_adam_AgencyFixedRateMember_documentation_en-US" xlink:label="lab_adam_AgencyFixedRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency Fixed Rate.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AgencyFixedRateMember" xlink:href="adam-20251231.xsd#adam_AgencyFixedRateMember"/>
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    <link:label id="lab_adam_ResidentialLoansMember_926bb18e-f4e4-454e-ae67-621321585384_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans</link:label>
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    <link:label id="lab_adam_ResidentialLoansMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoansMember" xlink:to="lab_adam_ResidentialLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_0673597d-cc05-4322-a1b0-bef7aa96d706_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateAccretionOfPurchaseDiscount_d9c46879-a567-4482-9049-5df0465facaf_terseLabel_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateAccretionOfPurchaseDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accretion of purchase discount</link:label>
    <link:label id="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateAccretionOfPurchaseDiscount_label_en-US" xlink:label="lab_adam_SECSchedule1229RealEstateCompaniesInvestmentInMortgageLoansOnRealEstateAccretionOfPurchaseDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Accretion Of Purchase Discount</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt_86bce720-6fdd-4f98-937f-0b4dd5b84ad2_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfUnsecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of senior unsecured notes, net</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentAxis_b086cc42-4dc0-4331-be5f-cb07f6b9a441_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NonCashFinancingActivitiesAbstract_bd92eb4b-6c69-4e13-9a6d-edc37b21437c_terseLabel_en-US" xlink:label="lab_adam_NonCashFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Cash Financing Activities:</link:label>
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    <link:label id="lab_adam_BetweenBBAndBCreditRatingMember_7fe969a3-68ed-4e2b-9897-ef2c896a4ccd_terseLabel_en-US" xlink:label="lab_adam_BetweenBBAndBCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Between BB+ And B+ Credit Rating</link:label>
    <link:label id="lab_adam_BetweenBBAndBCreditRatingMember_label_en-US" xlink:label="lab_adam_BetweenBBAndBCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Between BB+ And B+ Credit Rating [Member]</link:label>
    <link:label id="lab_adam_BetweenBBAndBCreditRatingMember_documentation_en-US" xlink:label="lab_adam_BetweenBBAndBCreditRatingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Between BB+ And B+ Credit Rating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_BetweenBBAndBCreditRatingMember" xlink:href="adam-20251231.xsd#adam_BetweenBBAndBCreditRatingMember"/>
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    <link:label id="lab_us-gaap_RentalIncomeNonoperating_d9d2b8c1-9c7e-4b76-9eb6-3e92b1225ee3_verboseLabel_en-US" xlink:label="lab_us-gaap_RentalIncomeNonoperating" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income from real estate</link:label>
    <link:label id="lab_us-gaap_RentalIncomeNonoperating_label_en-US" xlink:label="lab_us-gaap_RentalIncomeNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rental Income, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RentalIncomeNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RentalIncomeNonoperating"/>
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    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_2bb09e5e-2304-4360-a64d-bf2229e0f135_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019bf84d-4f6a-7225-802d-842c101c373b_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
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    <link:label id="lab_us-gaap_InvestmentBuildingAndBuildingImprovements_6df3c345-faf5-4293-86af-dd38aa82a042_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentBuildingAndBuildingImprovements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Building and improvements</link:label>
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    <link:label id="lab_adam_InvestmentPortfolioSegmentMember_019bf8a6-7dd6-7398-b68d-5a28f2d46db4_terseLabel_en-US" xlink:label="lab_adam_InvestmentPortfolioSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate/Other</link:label>
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    <link:label id="lab_adam_ReceivableFromDerivativeCounterparty_2a247e2b-509d-4fc1-a19b-d93155cacb00_terseLabel_en-US" xlink:label="lab_adam_ReceivableFromDerivativeCounterparty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivables from derivative counterparties</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedMortgagesMortgageBackedAndAssetBackedSecuritiesAtFairValue_0a2179d9-6149-457b-b23e-894568d38e13_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedMortgagesMortgageBackedAndAssetBackedSecuritiesAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans, at fair value</link:label>
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    <link:label id="lab_us-gaap_FinancialInstrumentsOwnedMortgagesMortgageBackedAndAssetBackedSecuritiesAtFairValue_460b5f6e-6548-4361-88c1-7c27b5a2a7da_netLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentsOwnedMortgagesMortgageBackedAndAssetBackedSecuritiesAtFairValue" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Residential loans, carrying value</link:label>
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    <link:label id="lab_adam_UnfundedCommitmentsForResidentialAndMultiFamilyInvestments_74934db1-1321-4d38-996f-29ba0b92ee18_terseLabel_en-US" xlink:label="lab_adam_UnfundedCommitmentsForResidentialAndMultiFamilyInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unfunded commitments for residential and multi-family investments</link:label>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_61600b85-0720-4c98-a83a-70ecb613cfd2_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross Amount of Recognized Assets (Liabilities)</link:label>
    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, before Offset</link:label>
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    <link:label id="lab_us-gaap_Land_8403b2ed-58e7-4532-b2f8-5efd344c16ec_terseLabel_en-US" xlink:label="lab_us-gaap_Land" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_Land_label_en-US" xlink:label="lab_us-gaap_Land" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land</link:label>
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    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_696e1442-a960-430d-bbb9-7692c9804655_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense on operating real estate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_PercentOfOutstandingSharesAffirmativeVotesMaterialAndAdverseChangesToPreferredStockTerms" xlink:href="adam-20251231.xsd#adam_PercentOfOutstandingSharesAffirmativeVotesMaterialAndAdverseChangesToPreferredStockTerms"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PercentOfOutstandingSharesAffirmativeVotesMaterialAndAdverseChangesToPreferredStockTerms" xlink:to="lab_adam_PercentOfOutstandingSharesAffirmativeVotesMaterialAndAdverseChangesToPreferredStockTerms" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_51ba8258-164b-4f35-8a06-26b2e161326f_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_370ef4a7-b222-46e3-95ac-77eee9dd2bbd_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">April&#160;30, 2023 - April&#160;29, 2024</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption, Period Two [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPeriodTwoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPeriodTwoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_A9.125SeniorNotesDue2030Member_7020c3b2-5e59-4c2c-a462-c6f0c6337c5b_terseLabel_en-US" xlink:label="lab_adam_A9.125SeniorNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">9.125% Senior Notes due 2030</link:label>
    <link:label id="lab_adam_A9.125SeniorNotesDue2030Member_label_en-US" xlink:label="lab_adam_A9.125SeniorNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">9.125% Senior Notes due 2030 [Member]</link:label>
    <link:label id="lab_adam_A9.125SeniorNotesDue2030Member_documentation_en-US" xlink:label="lab_adam_A9.125SeniorNotesDue2030Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">9.125% Senior Notes due 2030</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A9.125SeniorNotesDue2030Member" xlink:href="adam-20251231.xsd#adam_A9.125SeniorNotesDue2030Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_A9.125SeniorNotesDue2030Member" xlink:to="lab_adam_A9.125SeniorNotesDue2030Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_f8234522-99bd-4219-bf0f-ab445458ec86_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract_019c6568-1d92-7ed2-8f25-50051799f8cd_terseLabel_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification to disposal group held for sale</link:label>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract_label_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Reclassified To Held-For-Use [Abstract]</link:label>
    <link:label id="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract_documentation_en-US" xlink:label="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Reclassified To Held-For-Use</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:href="adam-20251231.xsd#adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:to="lab_adam_ImpairmentLongLivedAssetReclassifiedToHeldForUseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_c4f4c7e6-1f8d-4782-b641-356d5d0c2114_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_6079f51d-2979-43a9-9e1f-c4c5a317ad66_periodStartLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of period</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_11c807a8-5043-49c6-b54f-d7fe69e97434_periodEndLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at end of period</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_03861fcd-0f97-49dc-a0d6-1ed11b7e20b8_terseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_44023d1f-3644-4d56-baaf-a85634e9ad9f_verboseLabel_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights, estimated fair value</link:label>
    <link:label id="lab_us-gaap_ServicingAssetAtFairValueAmount_label_en-US" xlink:label="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Servicing Asset at Fair Value, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ServicingAssetAtFairValueAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ServicingAssetAtFairValueAmount" xlink:to="lab_us-gaap_ServicingAssetAtFairValueAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_ab308404-ae40-4d8b-adec-d45da7ac5df4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net amortization</link:label>
    <link:label id="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_label_en-US" xlink:label="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:to="lab_us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock_9ae175e6-9be1-4952-8eaf-1d5ea59754ef_terseLabel_en-US" xlink:label="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Special Purpose Entities (SPE) and Variable Interest Entities (VIE)</link:label>
    <link:label id="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use Of Special Purpose Entities And Variable Interest Entities [Text Block]</link:label>
    <link:label id="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock_documentation_en-US" xlink:label="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disclosure of special purpose entities and variable interest entities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:href="adam-20251231.xsd#adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:to="lab_adam_UseOfSpecialPurposeEntitiesAndVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount_e5f8ee5c-08db-443c-b681-143ae19a49f5_terseLabel_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum Aggregate Uncommitted Principal Amount</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount_label_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold Under Agreements to Repurchase, Maximum Repurchase Amount</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount_documentation_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The total amount of repossession that is available under the repurchase agreement.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:href="adam-20251231.xsd#adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:to="lab_adam_AssetsSoldUnderAgreementsToRepurchaseMaximumRepurchaseAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_ae44661e-6e72-4ce4-9018-b0c523f1e2c0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Key Term and Mortgage Payable in Consolidated VIE</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_91d683c6-e035-4540-9e34-28fa0c3df11c_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Granted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList_77dc5f01-8a50-4032-a732-dab60b9f1095_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Still Held, Unrealized Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList_label_en-US" xlink:label="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Asset, Recurring Basis, Still Held, Unrealized Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:to="lab_us-gaap_FairValueAssetRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_LouisvilleKYMember_54624b77-9fed-4eb5-a338-46553a715815_terseLabel_en-US" xlink:label="lab_adam_LouisvilleKYMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Louisville, KY</link:label>
    <link:label id="lab_adam_LouisvilleKYMember_label_en-US" xlink:label="lab_adam_LouisvilleKYMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Louisville, KY [Member]</link:label>
    <link:label id="lab_adam_LouisvilleKYMember_documentation_en-US" xlink:label="lab_adam_LouisvilleKYMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Louisville, KY</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_LouisvilleKYMember" xlink:href="adam-20251231.xsd#adam_LouisvilleKYMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_LouisvilleKYMember" xlink:to="lab_adam_LouisvilleKYMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DerivativeInstrumentsandHedgingActivitiesDisclosuresRollForward_dfabb56d-58c7-469f-8d77-160be90d2bc7_terseLabel_en-US" xlink:label="lab_adam_DerivativeInstrumentsandHedgingActivitiesDisclosuresRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Roll Forward]</link:label>
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    <link:label id="lab_adam_DerivativeInstrumentsandHedgingActivitiesDisclosuresRollForward_documentation_en-US" xlink:label="lab_adam_DerivativeInstrumentsandHedgingActivitiesDisclosuresRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Roll Forward]</link:label>
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    <link:label id="lab_adam_DerivativeAssetLiabilityNotionalAmount_898e5e23-4801-4417-88df-a57efd9d2803_periodStartLabel_en-US" xlink:label="lab_adam_DerivativeAssetLiabilityNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
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    <link:label id="lab_adam_DerivativeAssetLiabilityNotionalAmount_documentation_en-US" xlink:label="lab_adam_DerivativeAssetLiabilityNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Asset (Liability), Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DerivativeAssetLiabilityNotionalAmount" xlink:href="adam-20251231.xsd#adam_DerivativeAssetLiabilityNotionalAmount"/>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_69c8a6f2-df06-468c-8012-229cca7de5a5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Lease Intangibles</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
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    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
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    <link:label id="lab_us-gaap_MembersEquity_95748f02-4cbd-48f2-81f4-7643d6594f22_terseLabel_en-US" xlink:label="lab_us-gaap_MembersEquity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Members' equity</link:label>
    <link:label id="lab_us-gaap_MembersEquity_label_en-US" xlink:label="lab_us-gaap_MembersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Members' Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MembersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MembersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MembersEquity" xlink:to="lab_us-gaap_MembersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_NoncashOrPartNoncashAcquisitionConsolidationOfRealEstateHeld_97ee6da9-6811-4cc2-92ad-6561eea6df15_terseLabel_en-US" xlink:label="lab_adam_NoncashOrPartNoncashAcquisitionConsolidationOfRealEstateHeld" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation of real estate held in Consolidated VIEs</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_NoncashOrPartNoncashAcquisitionConsolidationOfRealEstateHeld" xlink:href="adam-20251231.xsd#adam_NoncashOrPartNoncashAcquisitionConsolidationOfRealEstateHeld"/>
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    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance_e64e75d1-0a64-4213-9ff9-49cb63efd096_verboseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contributions</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Increase from Subsidiary Equity Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestIncreaseFromSubsidiaryEquityIssuance"/>
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    <link:label id="lab_us-gaap_Maturity30To90DaysMember_5e768351-6a89-4a15-ae96-17ce05936c10_terseLabel_en-US" xlink:label="lab_us-gaap_Maturity30To90DaysMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over 30 days to 90 days</link:label>
    <link:label id="lab_us-gaap_Maturity30To90DaysMember_label_en-US" xlink:label="lab_us-gaap_Maturity30To90DaysMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maturity 30 to 90 Days [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Maturity30To90DaysMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Maturity30To90DaysMember"/>
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    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_f17aa6e5-13e1-4cc1-bc6b-db57b23d5292_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-Family Loans</link:label>
    <link:label id="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy_label_en-US" xlink:label="lab_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Held-for-Investment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLoanAndLeaseReceivablesHeldForInvestmentPolicy"/>
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    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_b6119157-f541-41e6-ac78-e04fcb9dc470_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Derivatives</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Derivatives [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock"/>
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    <link:label id="lab_srt_MortgageLoansOnRealEstateInterestRate_dc4cb6d6-e42e-445e-9463-a00876bc10c5_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateInterestRate_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate, Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateInterestRate" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateInterestRate"/>
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    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet_51557acb-84a9-4309-ba17-9af270389aa1_negatedTerseLabel_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net Deferred Finance Costs</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet_label_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Deferred Finance Costs, Net</link:label>
    <link:label id="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet_documentation_en-US" xlink:label="lab_adam_AssetsSoldUnderAgreementsToRepurchaseDeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Deferred Finance Costs, Net</link:label>
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    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndName"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted_019bf84d-4f6a-7162-b396-b9bbf705a5e1_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted pro forma earnings (loss) per common share (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted"/>
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    <link:label id="lab_adam_SwapMaturities2029Member_fa0167dd-98cf-4439-8330-23b01551af32_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2029Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_adam_SwapMaturities2029Member_label_en-US" xlink:label="lab_adam_SwapMaturities2029Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Swap Maturities 2029 [Member]</link:label>
    <link:label id="lab_adam_SwapMaturities2029Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2029Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2029</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2029Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2029Member"/>
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    <link:label id="lab_stpr_AR_d4467d01-1de2-49b6-8879-d5a97486a59d_terseLabel_en-US" xlink:label="lab_stpr_AR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arkansas</link:label>
    <link:label id="lab_stpr_AR_label_en-US" xlink:label="lab_stpr_AR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ARKANSAS</link:label>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsAbstract_019b0807-76b2-7df2-ac72-d0ed9a212966_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total gains/(losses) (realized/unrealized)</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsAbstract_e1ec3e74-795e-4347-9bfc-23b3bb67d705_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisGainLossIncludedInEarningsAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total losses/(gains) (realized/unrealized)</link:label>
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    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_019c22e9-374c-7ac5-ab77-a15ada9ff39d_terseLabel_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principle balance</link:label>
    <link:label id="lab_us-gaap_LoansHeldForSaleFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan, Held-for-Sale, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansHeldForSaleFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:to="lab_us-gaap_LoansHeldForSaleFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1_413a021e-495c-4f64-b72d-bd7bed0d9f51_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation of residential loans held in Consolidated SLST</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Other Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1" xlink:to="lab_us-gaap_NoncashOrPartNoncashAcquisitionOtherAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromRedemptions_69f7ea49-394b-40d3-aacc-a3175fde318e_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption of redeemable non-controlling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromRedemptions_c11b72bd-507c-4ebf-871a-eb616958912c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Redemption of redeemable non-controlling interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromRedemptions_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Redemptions or Purchase of Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestDecreaseFromRedemptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:to="lab_us-gaap_MinorityInterestDecreaseFromRedemptions" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock_019b0745-67ce-7340-a4b9-d3d82982c9e3_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Mortgage Banking Activities, Net</link:label>
    <link:label id="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock_label_en-US" xlink:label="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Components of Mortgage Banking Activities, Net [Table Text Block]</link:label>
    <link:label id="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock_documentation_en-US" xlink:label="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Components of Mortgage Banking Activities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:href="adam-20251231.xsd#adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:to="lab_adam_ScheduleOfComponentsOfMortgageBankingActivitiesNetTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_86250dd8-5952-41a7-b289-c3d5091e2ea4_netLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Outstanding Face Amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_45fe688b-1cf8-4417-ae81-923ae874a5b5_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt face amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MortgageLoansonRealEstateAdditionsAbstract_ff14fd35-f806-4a5f-8d4e-fa0fcc7ad643_terseLabel_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateAdditionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions during period:</link:label>
    <link:label id="lab_adam_MortgageLoansonRealEstateAdditionsAbstract_label_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateAdditionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Additions [Abstract]</link:label>
    <link:label id="lab_adam_MortgageLoansonRealEstateAdditionsAbstract_documentation_en-US" xlink:label="lab_adam_MortgageLoansonRealEstateAdditionsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Mortgage Loans on Real Estate, Additions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MortgageLoansonRealEstateAdditionsAbstract" xlink:href="adam-20251231.xsd#adam_MortgageLoansonRealEstateAdditionsAbstract"/>
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    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale_961644cf-c59c-4c8c-b843-6c22194e7b68_terseLabel_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transfer from disposal group held for sale</link:label>
    <link:label id="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale_label_en-US" xlink:label="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Transfers To Disposal Group Held For Sale</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale" xlink:href="adam-20251231.xsd#adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale" xlink:to="lab_adam_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersToDisposalGroupHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SingleFamilyRentalHeldForSaleMember_aee35c7d-761a-4be9-a3cd-0f0b53eca3d1_terseLabel_en-US" xlink:label="lab_adam_SingleFamilyRentalHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single-Family Rental - Held for Sale</link:label>
    <link:label id="lab_adam_SingleFamilyRentalHeldForSaleMember_label_en-US" xlink:label="lab_adam_SingleFamilyRentalHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single-Family Rental - Held for Sale [Member]</link:label>
    <link:label id="lab_adam_SingleFamilyRentalHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_SingleFamilyRentalHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Single-Family Rental - Held for Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SingleFamilyRentalHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_SingleFamilyRentalHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SingleFamilyRentalHeldForSaleMember" xlink:to="lab_adam_SingleFamilyRentalHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MarginDepositAssetExcessDeficitAmount_41dc13b3-c48a-424a-a23f-92ea4200e10b_terseLabel_en-US" xlink:label="lab_adam_MarginDepositAssetExcessDeficitAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Margin deposit asset, excess amount</link:label>
    <link:label id="lab_adam_MarginDepositAssetExcessDeficitAmount_label_en-US" xlink:label="lab_adam_MarginDepositAssetExcessDeficitAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Margin Deposit Asset, Excess (Deficit) Amount</link:label>
    <link:label id="lab_adam_MarginDepositAssetExcessDeficitAmount_documentation_en-US" xlink:label="lab_adam_MarginDepositAssetExcessDeficitAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Margin Deposit Asset, Excess (Deficit) Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MarginDepositAssetExcessDeficitAmount" xlink:href="adam-20251231.xsd#adam_MarginDepositAssetExcessDeficitAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MarginDepositAssetExcessDeficitAmount" xlink:to="lab_adam_MarginDepositAssetExcessDeficitAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_LucieAtTraditionHoldingsLLCMember_6e813929-da01-4393-b44b-6e47482e7549_terseLabel_en-US" xlink:label="lab_adam_LucieAtTraditionHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lucie at Tradition Holdings, LLC</link:label>
    <link:label id="lab_adam_LucieAtTraditionHoldingsLLCMember_label_en-US" xlink:label="lab_adam_LucieAtTraditionHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lucie at Tradition Holdings, LLC [Member]</link:label>
    <link:label id="lab_adam_LucieAtTraditionHoldingsLLCMember_documentation_en-US" xlink:label="lab_adam_LucieAtTraditionHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lucie at Tradition Holdings, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_LucieAtTraditionHoldingsLLCMember" xlink:href="adam-20251231.xsd#adam_LucieAtTraditionHoldingsLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_LucieAtTraditionHoldingsLLCMember" xlink:to="lab_adam_LucieAtTraditionHoldingsLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CMBSMember_03f67fa5-c7bb-4990-9519-d3d3ce138ca6_terseLabel_en-US" xlink:label="lab_adam_CMBSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">CMBS</link:label>
    <link:label id="lab_adam_CMBSMember_label_en-US" xlink:label="lab_adam_CMBSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CMBS [Member]</link:label>
    <link:label id="lab_adam_CMBSMember_documentation_en-US" xlink:label="lab_adam_CMBSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">CMBS.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CMBSMember" xlink:href="adam-20251231.xsd#adam_CMBSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CMBSMember" xlink:to="lab_adam_CMBSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_464efa97-4b93-4650-982f-8262762deb54_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue_019b9226-638e-7b2a-ae15-5cce0aed5bad_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Accumulated Change In Fair Value</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Accumulated Change In Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansAccumulatedChangeInFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:to="lab_adam_ResidentialMortgageLoansAccumulatedChangeInFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BankingAndThriftInterestAbstract_label_en-US" xlink:label="lab_us-gaap_BankingAndThriftInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Banking and Thrift, Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BankingAndThriftInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankingAndThriftInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BankingAndThriftInterestAbstract" xlink:to="lab_us-gaap_BankingAndThriftInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_e6046cbe-a8cb-4a68-9949-2b47d37f9fb9_periodStartLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Non-vested shares at beginning of period (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_ac731527-37bb-4406-9ef0-3522718ac163_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Non-vested shares at end of period (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShare_1521fea1-7311-4a92-908d-eb031633de87_terseLabel_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividend per share (in dollars per share)</link:label>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShare_label_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Taxable Dividend Per Share</link:label>
    <link:label id="lab_adam_CommonStockTaxableDividendPerShare_documentation_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The taxable dividends per share of common stock.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CommonStockTaxableDividendPerShare" xlink:href="adam-20251231.xsd#adam_CommonStockTaxableDividendPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_CommonStockTaxableDividendPerShare" xlink:to="lab_adam_CommonStockTaxableDividendPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SharebasedCompensationArrangementbySharebasedPaymentAwardFairValueAssumptionsExpectedTermforExpectedVolatilityRate_dd1d7a90-dd6d-421b-b816-63f58c8192da_terseLabel_en-US" xlink:label="lab_adam_SharebasedCompensationArrangementbySharebasedPaymentAwardFairValueAssumptionsExpectedTermforExpectedVolatilityRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected term for expected volatility rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_SharebasedCompensationArrangementbySharebasedPaymentAwardFairValueAssumptionsExpectedTermforExpectedVolatilityRate" xlink:href="adam-20251231.xsd#adam_SharebasedCompensationArrangementbySharebasedPaymentAwardFairValueAssumptionsExpectedTermforExpectedVolatilityRate"/>
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    <link:label id="lab_dei_IcfrAuditorAttestationFlag_19d09ab8-ba3b-4e7d-96e8-e6dbd630a422_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
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    <link:label id="lab_adam_MultiFamilyLoansMember_18e7aeeb-ebe6-4657-bd4d-18657266d651_terseLabel_en-US" xlink:label="lab_adam_MultiFamilyLoansMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family loans, at fair value</link:label>
    <link:label id="lab_adam_MultiFamilyLoansMember_label_en-US" xlink:label="lab_adam_MultiFamilyLoansMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi-Family Loans [Member]</link:label>
    <link:label id="lab_adam_MultiFamilyLoansMember_documentation_en-US" xlink:label="lab_adam_MultiFamilyLoansMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi-Family Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MultiFamilyLoansMember" xlink:href="adam-20251231.xsd#adam_MultiFamilyLoansMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MultiFamilyLoansMember" xlink:to="lab_adam_MultiFamilyLoansMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancingVIEsMember_2ff4cb6e-b941-4380-ada5-ed1354b56b4f_terseLabel_en-US" xlink:label="lab_adam_FinancingVIEsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing VIE's</link:label>
    <link:label id="lab_adam_FinancingVIEsMember_label_en-US" xlink:label="lab_adam_FinancingVIEsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing VIE's [Member]</link:label>
    <link:label id="lab_adam_FinancingVIEsMember_documentation_en-US" xlink:label="lab_adam_FinancingVIEsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing VIE's</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingVIEsMember" xlink:href="adam-20251231.xsd#adam_FinancingVIEsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancingVIEsMember" xlink:to="lab_adam_FinancingVIEsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancingReceivableOriginationCosts_019bf8a6-7dd6-7874-98f4-10610bef4b47_verboseLabel_en-US" xlink:label="lab_adam_FinancingReceivableOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loan origination costs</link:label>
    <link:label id="lab_adam_FinancingReceivableOriginationCosts_label_en-US" xlink:label="lab_adam_FinancingReceivableOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Origination Costs</link:label>
    <link:label id="lab_adam_FinancingReceivableOriginationCosts_documentation_en-US" xlink:label="lab_adam_FinancingReceivableOriginationCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Origination Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingReceivableOriginationCosts" xlink:href="adam-20251231.xsd#adam_FinancingReceivableOriginationCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancingReceivableOriginationCosts" xlink:to="lab_adam_FinancingReceivableOriginationCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepurchaseAgreementsMember_c0078d52-8d40-4d03-a040-79f94f0b8927_terseLabel_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase agreements and warehouse facilities</link:label>
    <link:label id="lab_us-gaap_RepurchaseAgreementsMember_label_en-US" xlink:label="lab_us-gaap_RepurchaseAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepurchaseAgreementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RepurchaseAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepurchaseAgreementsMember" xlink:to="lab_us-gaap_RepurchaseAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_a3118ebb-8241-40ce-8301-e133edda13d6_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorFirmId_eff39548-0d22-483b-a506-4ff3f6f35aa3_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:label id="lab_dei_AuditorFirmId_label_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorFirmId" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorFirmId"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorFirmId" xlink:to="lab_dei_AuditorFirmId" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019bf8a6-7dd6-71bd-a7b2-ffafa6844a50_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_c8373ad9-106a-4162-983e-63e412fcb644_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Securities Available For Sale, at Fair Value</link:label>
    <link:label id="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption_5c31e3d3-3865-4318-ba15-24732d495d73_terseLabel_en-US" xlink:label="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from residential loan securitization redemption</link:label>
    <link:label id="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption_label_en-US" xlink:label="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Residential Loan Securitization Redemption</link:label>
    <link:label id="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption_documentation_en-US" xlink:label="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Residential Loan Securitization Redemption</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:href="adam-20251231.xsd#adam_ProceedsFromResidentialLoanSecuritizationRedemption"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:to="lab_adam_ProceedsFromResidentialLoanSecuritizationRedemption" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain_d4603d55-0fc8-4848-ae3c-a586567fa183_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Sold under Agreements to Repurchase, Maturity Period [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain_label_en-US" xlink:label="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Agreements and Similar Transactions, Maturity Periods [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain" xlink:to="lab_us-gaap_AssetsSoldUnderAgreementsToRepurchaseMaturityPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_90ca9ca0-be43-4461-aecf-fec014fbf745_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesInvestments_019c2ea4-17eb-770e-a2ed-6ef599e5a04c_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities available for sale</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesInvestments_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesInvestments" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_7376a3dd-178e-4b68-b7f1-7e5b3b797239_terseLabel_en-US" xlink:label="lab_adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Liability Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
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    <link:label id="lab_adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Liability Gain Loss Statement Of Income Extensible List Not Disclosed Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag" xlink:href="adam-20251231.xsd#adam_FairValueRecurringBasisUnobservableInputReconciliationLiabilityGainLossStatementOfIncomeExtensibleListNotDisclosedFlag"/>
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    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_86076746-f770-4050-a7db-00cce040d546_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_label_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BalanceSheetLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BalanceSheetLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BalanceSheetLocationDomain" xlink:to="lab_us-gaap_BalanceSheetLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract_019c2ea5-ab65-78a5-a4c8-c6ad0b29eceb_terseLabel_en-US" xlink:label="lab_adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GAAP/Tax differences</link:label>
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    <link:label id="lab_adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract_documentation_en-US" xlink:label="lab_adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, GAAP/Tax basis differences</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract" xlink:href="adam-20251231.xsd#adam_DeferredTaxLiabilitiesGAAPTaxBasisDifferencesAbstract"/>
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    <link:label id="lab_adam_UnderwrittenPublicOfferingMember_1247b5dc-3082-4a2a-a845-bf04c0ecc873_terseLabel_en-US" xlink:label="lab_adam_UnderwrittenPublicOfferingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underwritten Public Offering</link:label>
    <link:label id="lab_adam_UnderwrittenPublicOfferingMember_label_en-US" xlink:label="lab_adam_UnderwrittenPublicOfferingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underwritten Public Offering [Member]</link:label>
    <link:label id="lab_adam_UnderwrittenPublicOfferingMember_documentation_en-US" xlink:label="lab_adam_UnderwrittenPublicOfferingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Underwritten Public Offering [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnderwrittenPublicOfferingMember" xlink:href="adam-20251231.xsd#adam_UnderwrittenPublicOfferingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnderwrittenPublicOfferingMember" xlink:to="lab_adam_UnderwrittenPublicOfferingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_1a27cd39-8d6d-4096-afe1-f3a845aef8c3_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsAbstract" xlink:to="lab_us-gaap_DerivativeAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate_a802ca44-102b-4f06-a426-28d844b2f4a5_terseLabel_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate_label_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Non-controlling Interest, Weighted Average Discount Rate</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate_documentation_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redeemable Non-controlling Interest, Weighted Average Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:href="adam-20251231.xsd#adam_RedeemableNonControllingInterestWeightedAverageDiscountRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:to="lab_adam_RedeemableNonControllingInterestWeightedAverageDiscountRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_7d91fff5-8a69-441b-b288-04f06e8924ed_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings (Loss) Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:to="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MarginPayableToDerivativeCounterparties_019b07cc-3b81-700e-be83-d208b65fbf04_terseLabel_en-US" xlink:label="lab_adam_MarginPayableToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Margin payable to derivative counterparties</link:label>
    <link:label id="lab_adam_MarginPayableToDerivativeCounterparties_label_en-US" xlink:label="lab_adam_MarginPayableToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Margin Payable To Derivative Counterparties</link:label>
    <link:label id="lab_adam_MarginPayableToDerivativeCounterparties_documentation_en-US" xlink:label="lab_adam_MarginPayableToDerivativeCounterparties" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Margin Payable To Derivative Counterparties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MarginPayableToDerivativeCounterparties" xlink:href="adam-20251231.xsd#adam_MarginPayableToDerivativeCounterparties"/>
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    <link:label id="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities_e876dca4-822f-41c6-b5e6-f92bd3daaaba_terseLabel_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redeemable Non-Controlling Interest in Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities_46c3b52c-3b99-445b-b2f2-8b2724eb96db_verboseLabel_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Redeemable non-controlling interest in consolidated variable interest entities</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities_label_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Redeemable Non-Controlling Interest In Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities_documentation_en-US" xlink:label="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Redeemable Non-Controlling Interest In Consolidated Variable Interest Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:href="adam-20251231.xsd#adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:to="lab_adam_RedeemableNonControllingInterestInConsolidatedVariableInterestEntities" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_PreferredStockSeriesSharesMember_26a6d050-3ce3-4c77-b27a-bfe77f375d2f_terseLabel_en-US" xlink:label="lab_adam_PreferredStockSeriesSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred Stock Series Shares</link:label>
    <link:label id="lab_adam_PreferredStockSeriesSharesMember_label_en-US" xlink:label="lab_adam_PreferredStockSeriesSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Series Shares [Member]</link:label>
    <link:label id="lab_adam_PreferredStockSeriesSharesMember_documentation_en-US" xlink:label="lab_adam_PreferredStockSeriesSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Series Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredStockSeriesSharesMember" xlink:href="adam-20251231.xsd#adam_PreferredStockSeriesSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_PreferredStockSeriesSharesMember" xlink:to="lab_adam_PreferredStockSeriesSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember_019c2856-fbcf-78bb-bedd-590c8760eb28_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans, residential loans held in securitization trusts and residential loans held for sale</link:label>
    <link:label id="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember_label_en-US" xlink:label="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loans, Residential Loans Held In Securitization Trusts And Residential Mortgage Loans Held-For-Sale [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loans, Residential Loans Held In Securitization Trusts And Residential Mortgage Loans Held-For-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:to="lab_adam_ResidentialLoansResidentialLoansHeldInSecuritizationTrustsAndResidentialMortgageLoansHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseAbstract_1d18ee7b-88d5-4c31-93bb-f2b68227cb22_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GENERAL, ADMINISTRATIVE AND OPERATING EXPENSES:</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpenseAbstract" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_1c10a021-f105-4816-abed-621a4e6a62ed_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts Offset in Balance Sheets</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, Asset Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityFairValueGrossAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:to="lab_us-gaap_DerivativeLiabilityFairValueGrossAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_dd6ac57f-3ef1-4b94-91a3-dd22e63b5804_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of investment securities</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_8ed753dd-e0c8-4149-bc92-0b7c740b033b_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value $0.01 per share, 31,500,000 shares authorized, 22,385,674 and 22,164,414 shares issued and outstanding as of December&#160;31, 2025 and December&#160;31, 2024, respectively ($559,642 and $554,110 aggregate liquidation preference as of December&#160;31, 2025 and December&#160;31, 2024, respectively)</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_b1f3ca74-d764-40c6-8b77-c37acbb1fead_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue"/>
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    <link:label id="lab_adam_MeasurementInputYieldMember_43495431-a720-418a-bc67-7568a497c732_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputYieldMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Yield</link:label>
    <link:label id="lab_adam_MeasurementInputYieldMember_label_en-US" xlink:label="lab_adam_MeasurementInputYieldMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Yield [Member]</link:label>
    <link:label id="lab_adam_MeasurementInputYieldMember_documentation_en-US" xlink:label="lab_adam_MeasurementInputYieldMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input Yield</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputYieldMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputYieldMember"/>
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    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_6c9b204b-5098-4e08-a415-76f5cfe69208_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest payable</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrentAndNoncurrent"/>
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    <link:label id="lab_us-gaap_SubordinatedDebt_4d71cae0-3ce5-4fa7-9226-88019cdc67d4_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated debentures</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebt_3e78896e-878a-49b2-9fd8-33e04d8f9552_verboseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebt" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Subordinated debentures, carrying value</link:label>
    <link:label id="lab_us-gaap_SubordinatedDebt_label_en-US" xlink:label="lab_us-gaap_SubordinatedDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubordinatedDebt" xlink:to="lab_us-gaap_SubordinatedDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_019bf84d-4f6a-7ff7-84d0-8d5733584007_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
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    <link:label id="lab_us-gaap_SubordinatedDebtMember_b3ad4535-a1f1-497f-8dcd-a6a134648d2d_terseLabel_en-US" xlink:label="lab_us-gaap_SubordinatedDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated debentures</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubordinatedDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubordinatedDebtMember"/>
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    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_1d6f781b-f74e-4429-9919-9d7aff523c54_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Asset, Period Past Due [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis_label_en-US" xlink:label="lab_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Aging [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivablesPeriodPastDueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivablesPeriodPastDueAxis"/>
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    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_2b8170fd-3468-43aa-97e7-83ee8ee9f8d3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
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    <link:label id="lab_adam_RepurchaseAgreementsWeightedAverageAdvanceRate_da1cca27-9607-4195-a59d-54892d21c916_terseLabel_en-US" xlink:label="lab_adam_RepurchaseAgreementsWeightedAverageAdvanceRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average advance rate</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_f44ff4db-9cd9-43ed-a8ce-b51634d5dbce_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value $0.01 per share, 200,000,000 shares authorized, 90,303,863 and 90,574,996 shares issued and outstanding as of December&#160;31, 2025 and December&#160;31, 2024, respectively</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
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    <link:label id="lab_adam_AssetsHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_AssetsHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AssetsHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_AssetsHeldForSaleMember"/>
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    <link:label id="lab_us-gaap_ShareBasedPaymentArrangementEmployeeMember_0d33b515-f0cb-437e-8c02-aba48a1ba49f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedPaymentArrangementEmployeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee</link:label>
    <link:label id="lab_us-gaap_ShareBasedPaymentArrangementEmployeeMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedPaymentArrangementEmployeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Employee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedPaymentArrangementEmployeeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedPaymentArrangementEmployeeMember"/>
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    <link:label id="lab_adam_SwapMaturities2045Member_019c2c36-f350-71f8-966d-247642f7bbcf_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2045Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2045</link:label>
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    <link:label id="lab_adam_SwapMaturities2045Member_documentation_en-US" xlink:label="lab_adam_SwapMaturities2045Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Swap Maturities 2045</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SwapMaturities2045Member" xlink:href="adam-20251231.xsd#adam_SwapMaturities2045Member"/>
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    <link:label id="lab_adam_LittleRockARMember_92674e04-b8d1-40c3-bc57-e76157ada544_terseLabel_en-US" xlink:label="lab_adam_LittleRockARMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Little Rock, AR</link:label>
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    <link:label id="lab_adam_LittleRockARMember_documentation_en-US" xlink:label="lab_adam_LittleRockARMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Little Rock, AR</link:label>
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    <link:label id="lab_srt_TitleOfIndividualAxis_5a95ecf3-e2d7-4bbc-98a3-cf651b5b4cee_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:label id="lab_srt_TitleOfIndividualAxis_label_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_c5c6b549-5a7a-40ec-8d4c-49bd0fe4d72b_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies (See Note 16)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
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    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_f56b838b-64ee-4bb9-b0bf-220dc98edfaf_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation Preference</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreferenceValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Liquidation Preference, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreferenceValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockLiquidationPreferenceValue"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019be5a9-a7d3-7049-a21b-74b3dcafa57f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_adam_EquityAndMezzanineLoansFairValue1_label_en-US" xlink:label="lab_adam_EquityAndMezzanineLoansFairValue1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity and Mezzanine Loans, Fair Value1</link:label>
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    <link:label id="lab_adam_BusinessCombinationRecognizedAssetAcquiredResidentialMortgageLoansHeldForSale_019bf84d-4f6a-700e-9e29-1800717b2fc4_terseLabel_en-US" xlink:label="lab_adam_BusinessCombinationRecognizedAssetAcquiredResidentialMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held for sale</link:label>
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    <link:label id="lab_adam_MultiFamilyLoansAtFairValueTextBlock_56e5d102-368a-44a7-9fcd-7261157b32d7_terseLabel_en-US" xlink:label="lab_adam_MultiFamilyLoansAtFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family Loans, at Fair Value</link:label>
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    <link:label id="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount_c4a350c0-8005-4a9b-b349-8f8c67bc46f4_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageLoansInProcessOfForeclosureAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Process of foreclosure</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet_9495b2c1-2ce0-45f2-a826-9fc6c4158234_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total net deferred tax asset</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_019c2f12-7769-7ca8-ab78-5f0c8fd4ef3a_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">10+ years</link:label>
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    <link:label id="lab_adam_NYMPreferredTrustIMember_documentation_en-US" xlink:label="lab_adam_NYMPreferredTrustIMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">NYM Preferred Trust I.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_NYMPreferredTrustIMember" xlink:href="adam-20251231.xsd#adam_NYMPreferredTrustIMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_NYMPreferredTrustIMember" xlink:to="lab_adam_NYMPreferredTrustIMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_d03891e1-61ce-4540-9fdf-b9d7025afccb_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_HedgingDesignationAxis"/>
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    <link:label id="lab_adam_OtherReceivablesMember_8c070ec3-11f9-4ea9-875e-6e0af89691d0_terseLabel_en-US" xlink:label="lab_adam_OtherReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
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    <link:label id="lab_adam_OtherReceivablesMember_documentation_en-US" xlink:label="lab_adam_OtherReceivablesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Receivables</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OtherReceivablesMember" xlink:href="adam-20251231.xsd#adam_OtherReceivablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_OtherReceivablesMember" xlink:to="lab_adam_OtherReceivablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock_d8c44a63-1de1-4df6-b53b-8bc3626483aa_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock" xlink:to="lab_us-gaap_OtherNonoperatingIncomeAndExpenseTextBlock" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilityRecurringBasisStillHeldUnrealizedGainLossStatementOfIncomeExtensibleList"/>
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    <link:label id="lab_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue_94be2bf4-ae94-4e3c-8f83-e6d76dfae840_terseLabel_en-US" xlink:label="lab_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations at fair value</link:label>
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    <link:label id="lab_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue_documentation_en-US" xlink:label="lab_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Securities, Residential Loan Securitizations at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue" xlink:href="adam-20251231.xsd#adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue" xlink:to="lab_adam_DebtSecuritiesResidentialLoanSecuritizationsAtFairValue" xlink:type="arc" order="1"/>
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    <link:label id="lab_adam_A1122ChicagoDELLCMember_75e06fd9-247e-46c6-9074-34f29903cfe2_terseLabel_en-US" xlink:label="lab_adam_A1122ChicagoDELLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">1122 Chicago DE, LLC</link:label>
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    <link:label id="lab_adam_A1122ChicagoDELLCMember_documentation_en-US" xlink:label="lab_adam_A1122ChicagoDELLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">1122 Chicago DE, LLC</link:label>
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    <link:label id="lab_adam_ReceivablesAndOtherAssets_2dd5214c-8f85-4b9a-960a-9a313d4a9db9_terseLabel_en-US" xlink:label="lab_adam_ReceivablesAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-family loans, carrying value</link:label>
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    <link:label id="lab_stpr_CA_dceec5e1-69bc-418a-ac4f-4d713d2865a7_terseLabel_en-US" xlink:label="lab_stpr_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">California</link:label>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_0b816587-8998-4c9b-9555-d8b9ab9d54a0_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_b41587f1-2b01-437d-84ff-a42ace186150_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Requisite service period</link:label>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_5704f2dc-e98b-4dfe-a92c-f6c029228ea7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized Losses</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_e618e415-e3c3-4b83-b4ca-e03aaa1dfa50_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_9ae6aeda-aedd-4438-8058-785e0f0cb774_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of and capital expenditures on real estate</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
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    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
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    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_2ef4d622-bf14-4fd2-a3e0-df823bfcfa0b_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized Gains (Losses)</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnDerivatives_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnDerivatives" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Derivatives</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnDerivatives" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnDerivatives"/>
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    <link:label id="lab_adam_OtherRealEstateExpense_4853b8e4-6ee2-4b33-98d7-1288ad67383f_terseLabel_en-US" xlink:label="lab_adam_OtherRealEstateExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other real estate expenses</link:label>
    <link:label id="lab_adam_OtherRealEstateExpense_label_en-US" xlink:label="lab_adam_OtherRealEstateExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Real Estate Expense</link:label>
    <link:label id="lab_adam_OtherRealEstateExpense_documentation_en-US" xlink:label="lab_adam_OtherRealEstateExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Real Estate Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_OtherRealEstateExpense" xlink:href="adam-20251231.xsd#adam_OtherRealEstateExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_OtherRealEstateExpense" xlink:to="lab_adam_OtherRealEstateExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_f7d7c533-b238-4364-910e-843fc4f5bccd_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_6125dc6b-cbb3-467f-b72c-8c2772b19040_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate (as a percent)</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember_5b0c01a3-e1d6-4e01-8843-28d5c82f2979_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations at amortized cost, net</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember_label_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loan Securitizations at Amortized Cost, Net [Member]</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember_documentation_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loan Securitizations at Amortized Cost, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:href="adam-20251231.xsd#adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:to="lab_adam_ResidentialLoanSecuritizationsAtAmortizedCostNetMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_InterestRateStepUpMember_082d4c8b-c552-409a-b29e-3a18f9804017_terseLabel_en-US" xlink:label="lab_adam_InterestRateStepUpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up</link:label>
    <link:label id="lab_adam_InterestRateStepUpMember_label_en-US" xlink:label="lab_adam_InterestRateStepUpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up [Member]</link:label>
    <link:label id="lab_adam_InterestRateStepUpMember_documentation_en-US" xlink:label="lab_adam_InterestRateStepUpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Step-Up</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_InterestRateStepUpMember" xlink:href="adam-20251231.xsd#adam_InterestRateStepUpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_InterestRateStepUpMember" xlink:to="lab_adam_InterestRateStepUpMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue_95b6d860-3d3f-46f5-9279-802031cc672f_verboseLabel_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans, at fair value</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue_label_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Residential Loans At Fair Value</link:label>
    <link:label id="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue_documentation_en-US" xlink:label="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Instruments Owned, Residential Loans At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:href="adam-20251231.xsd#adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:to="lab_adam_FinancialInstrumentsOwnedResidentialLoansAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_cd127b21-d4a5-4aea-b549-334f794c7da7_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other liabilities</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_9a3af04f-e08c-4e36-a34e-269deb0a06d4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Gross Derivative Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDerivativeInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_ce943bbd-1bef-4ffe-b653-8a2fcec4a0f4_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate sales</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_0ffea4dd-78f1-47e3-b0d8-733c78eff5cb_verboseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of real estate</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfProperties_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfProperties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfProperties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfProperties"/>
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    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_019bf84d-4f6a-7de1-8ec4-994ff812f4c9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTable"/>
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    <link:label id="lab_us-gaap_GainLossOnSaleOfOtherInvestments_feac3045-1368-4b5c-8a05-c79848a83aee_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized losses, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfOtherInvestments_019c222d-1327-7a49-adab-bb4b0930df6c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Realized losses, net</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfOtherInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfOtherInvestments"/>
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    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_fe7a0f72-cecc-4ae2-bec1-001858258e5b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Fixed Interest Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeAverageFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeAverageFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Average Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAverageFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAverageFixedInterestRate"/>
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    <link:label id="lab_srt_StatementGeographicalAxis_8963b442-f361-4e56-8ffe-67d491011d95_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
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    <link:label id="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet_019b0710-d117-72ad-858d-f58d558a7aed_terseLabel_en-US" xlink:label="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock based compensation expense (benefit), net</link:label>
    <link:label id="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet_label_en-US" xlink:label="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, After Forfeiture, Net</link:label>
    <link:label id="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet_documentation_en-US" xlink:label="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, After Forfeiture, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:href="adam-20251231.xsd#adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:to="lab_adam_SharesIssuedValueShareBasedPaymentArrangementAfterForfeitureNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_d145917c-dd12-4f90-b1e7-f798843ce22a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities:</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesAbstract" xlink:to="lab_us-gaap_DerivativeLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_bcbe86e2-005e-47c0-a050-9552048513ed_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MeasurementInputLiquidationTimelinePeriodMember_6dd22795-1547-4b8d-9573-a7c7ee6a3a46_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liquidation timeline (months)</link:label>
    <link:label id="lab_adam_MeasurementInputLiquidationTimelinePeriodMember_label_en-US" xlink:label="lab_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Liquidation Timeline Period [Member]</link:label>
    <link:label id="lab_adam_MeasurementInputLiquidationTimelinePeriodMember_documentation_en-US" xlink:label="lab_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input Liquidation Timeline Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:href="adam-20251231.xsd#adam_MeasurementInputLiquidationTimelinePeriodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:to="lab_adam_MeasurementInputLiquidationTimelinePeriodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_019bf84d-4f6a-77cc-b810-3fc923b9c670_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtFairValue_17705d1b-1dad-4298-a25c-f957cdb86e45_terseLabel_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loan securitizations at fair value, carrying value</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtFairValue_label_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Loan Securitizations at Fair Value</link:label>
    <link:label id="lab_adam_ResidentialLoanSecuritizationsAtFairValue_documentation_en-US" xlink:label="lab_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Loan Securitizations at Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:href="adam-20251231.xsd#adam_ResidentialLoanSecuritizationsAtFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:to="lab_adam_ResidentialLoanSecuritizationsAtFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_A2029SeniorNotesMember_7555ae9b-649e-4d9f-8d98-cfdfb9bdb003_terseLabel_en-US" xlink:label="lab_adam_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029 Senior Notes</link:label>
    <link:label id="lab_adam_A2029SeniorNotesMember_label_en-US" xlink:label="lab_adam_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2029 Senior Notes [Member]</link:label>
    <link:label id="lab_adam_A2029SeniorNotesMember_documentation_en-US" xlink:label="lab_adam_A2029SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2029 Senior Notes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_A2029SeniorNotesMember" xlink:href="adam-20251231.xsd#adam_A2029SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_A2029SeniorNotesMember" xlink:to="lab_adam_A2029SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards_8fbab59e-b2bd-4b49-ad45-362de553a684_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital loss carryover</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Capital Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsCapitalLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards" xlink:to="lab_us-gaap_DeferredTaxAssetsCapitalLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_ffd5bc43-3d6a-48bb-ac4c-9287435b7cc8_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_5e532ef2-a1c6-4b05-a9d7-b329726d9981_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MortgageLoansOnRealEstateScheduleTable_23819034-de5b-4490-aba6-d2d1db197e93_terseLabel_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateScheduleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate Schedule [Table]</link:label>
    <link:label id="lab_srt_MortgageLoansOnRealEstateScheduleTable_label_en-US" xlink:label="lab_srt_MortgageLoansOnRealEstateScheduleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-29, Real Estate Companies, Investment in Mortgage Loans on Real Estate Schedule [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MortgageLoansOnRealEstateScheduleTable" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MortgageLoansOnRealEstateScheduleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MortgageLoansOnRealEstateScheduleTable" xlink:to="lab_srt_MortgageLoansOnRealEstateScheduleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_16ab9eb7-3cbc-4b24-b9a4-99f8766a0d4b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_019c28b9-20a0-7bf1-a6b1-fc60192ad8d3_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareBasicLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:to="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SingleFamilyRentalPropertiesMember_1bbdced1-281e-4dc5-8416-343a3438ec71_terseLabel_en-US" xlink:label="lab_adam_SingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single-family rental properties</link:label>
    <link:label id="lab_adam_SingleFamilyRentalPropertiesMember_label_en-US" xlink:label="lab_adam_SingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single-Family Rental Properties [Member]</link:label>
    <link:label id="lab_adam_SingleFamilyRentalPropertiesMember_documentation_en-US" xlink:label="lab_adam_SingleFamilyRentalPropertiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Single-Family Rental Properties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SingleFamilyRentalPropertiesMember" xlink:href="adam-20251231.xsd#adam_SingleFamilyRentalPropertiesMember"/>
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    <link:label id="lab_us-gaap_EarningsPerShareAbstract_20cc2c1c-5fae-4de8-b14e-7b8be210d7bf_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_20d2f254-214e-4127-b15b-7157e0218144_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeCapInterestRate_687c0111-9eaa-45bc-b83a-09bcf8d37198_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeCapInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SOFR Strike Price</link:label>
    <link:label id="lab_us-gaap_DerivativeCapInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeCapInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Cap Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeCapInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeCapInterestRate"/>
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    <link:label id="lab_adam_NetRealizedGainLossOnPayoffOfMortgageLoans_label_en-US" xlink:label="lab_adam_NetRealizedGainLossOnPayoffOfMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Realized Gain (Loss) On Payoff Of Mortgage Loans</link:label>
    <link:label id="lab_adam_NetRealizedGainLossOnPayoffOfMortgageLoans_documentation_en-US" xlink:label="lab_adam_NetRealizedGainLossOnPayoffOfMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net Realized Gain (Loss) On Payoff Of Mortgage Loans</link:label>
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    <link:label id="lab_adam_ResidentialMortgageLoansPremiumDiscountAmount_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansPremiumDiscountAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Premium (Discount) Amount</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansPremiumDiscountAmount_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansPremiumDiscountAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Premium (Discount) Amount</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019be5a9-d5f8-79b9-b832-ba7abcee197a_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
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    <link:label id="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital_label_en-US" xlink:label="lab_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Equity Method Investment, Distribution, Return of Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromEquityMethodInvestmentDividendsOrDistributionsReturnOfCapital"/>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesMortgageServicingRights_019c2ea4-17eb-76ef-8efe-dcb2c3a24e6f_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgage servicing rights</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesMortgageServicingRights_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesMortgageServicingRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Mortgage Servicing Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesMortgageServicingRights" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesMortgageServicingRights"/>
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    <link:label id="lab_adam_SanAntonioTX2Member_dc16852e-642c-484e-8674-ac77ee2d0729_terseLabel_en-US" xlink:label="lab_adam_SanAntonioTX2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">San Antonio, TX</link:label>
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    <link:label id="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock_66c0ec98-e28a-47b7-abed-c3b06f7caa31_terseLabel_en-US" xlink:label="lab_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Components of Interest Income and Interest Expense</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestIncomeAndInterestExpenseDisclosureTableTextBlock"/>
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    <link:label id="lab_us-gaap_DebtInstrumentRepaidPrincipal_019c4dd6-63e5-765f-b149-61094d96aecb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRepaidPrincipal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt principal repaid</link:label>
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    <link:label id="lab_adam_EquityandMezzanineLoansFairValue_019c2856-fbcf-79eb-b2e6-dc8ed1b72d84_terseLabel_en-US" xlink:label="lab_adam_EquityandMezzanineLoansFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_adam_EquityandMezzanineLoansFairValue_label_en-US" xlink:label="lab_adam_EquityandMezzanineLoansFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity and Mezzanine Loans, Fair Value</link:label>
    <link:label id="lab_adam_EquityandMezzanineLoansFairValue_documentation_en-US" xlink:label="lab_adam_EquityandMezzanineLoansFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity and Mezzanine Loans, Fair Value</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
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    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingAxis_f4f1dafc-249a-4efc-92ef-cbd404665bd3_terseLabel_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Axis]</link:label>
    <link:label id="lab_us-gaap_ExternalCreditRatingByGroupingAxis_label_en-US" xlink:label="lab_us-gaap_ExternalCreditRatingByGroupingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating by Grouping [Axis]</link:label>
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    <link:label id="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets_9bfeed00-fbb8-44a3-9fce-150648718788_totalLabel_en-US" xlink:label="lab_us-gaap_ContractuallySpecifiedServicingFeesLateFeesAndAncillaryFeesEarnedInExchangeForServicingFinancialAssets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Servicing fee income</link:label>
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    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
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    <link:label id="lab_adam_DefeasanceCosts_label_en-US" xlink:label="lab_adam_DefeasanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defeasance Costs</link:label>
    <link:label id="lab_adam_DefeasanceCosts_documentation_en-US" xlink:label="lab_adam_DefeasanceCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Defeasance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_DefeasanceCosts" xlink:href="adam-20251231.xsd#adam_DefeasanceCosts"/>
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    <link:label id="lab_us-gaap_MeasurementInputLossSeverityMember_7d184dec-a635-4250-a881-4fe78a55f3d8_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputLossSeverityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss severity</link:label>
    <link:label id="lab_us-gaap_MeasurementInputLossSeverityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputLossSeverityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Loss Severity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputLossSeverityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputLossSeverityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputLossSeverityMember" xlink:to="lab_us-gaap_MeasurementInputLossSeverityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_d19d68cf-1146-48e9-aff5-d3ae5a735067_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase_34606896-f83c-42b9-88b6-c0d5e219b989_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net proceeds received from repurchase agreements and warehouse facilities</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payments for) in Securities Sold under Agreements to Repurchase</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForInSecuritiesSoldUnderAgreementsToRepurchase"/>
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    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_a8acfd79-0cd4-43cb-9bdc-38b2eb962289_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred State and Local Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredStateAndLocalIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_stpr_IN_95f7e774-a5d4-40ba-aee8-312961b3f8a3_terseLabel_en-US" xlink:label="lab_stpr_IN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indiana</link:label>
    <link:label id="lab_stpr_IN_label_en-US" xlink:label="lab_stpr_IN" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">INDIANA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_IN" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_IN"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_019c22e9-374c-7259-876a-014f49a3631d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Principal balance of loans sold to third parties</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale, Loan, Mortgage, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:to="lab_us-gaap_ProceedsFromSaleOfMortgageLoansHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_IL_7a913856-6810-4ae0-8888-60cdc2d74120_terseLabel_en-US" xlink:label="lab_stpr_IL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Illinois</link:label>
    <link:label id="lab_stpr_IL_label_en-US" xlink:label="lab_stpr_IL" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ILLINOIS</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_stpr_IL" xlink:href="https://xbrl.sec.gov/stpr/2025/stpr-2025.xsd#stpr_IL"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_stpr_IL" xlink:to="lab_stpr_IL" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_5da21277-69b3-4f38-8243-10514b15f374_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">NET INCOME (LOSS) ATTRIBUTABLE TO COMPANY</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019be4da-6ff1-7140-9121-6a32ed7ae797_netLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total net gains attributable to Company's common shareholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_d391d326-0738-4136-91fc-c1df339ba24d_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) attributable to Company</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTable_e70f2193-605c-4688-8543-73afa2925334_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTable_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTable" xlink:to="lab_us-gaap_SubsequentEventTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_6907051a-c889-410f-bc5e-d30fbc1e1bd9_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Nonconsolidated Investee [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:to="lab_us-gaap_EquityMethodInvestmentNonconsolidatedInvesteeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_ed3b6cef-896b-4b0f-9ebe-302934a69d0c_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_d01cf988-c990-42d6-8df5-97b530e102eb_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating real estate, net</link:label>
    <link:label id="lab_us-gaap_RealEstateInvestmentPropertyNet_label_en-US" xlink:label="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investment Property, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RealEstateInvestmentPropertyNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RealEstateInvestmentPropertyNet" xlink:to="lab_us-gaap_RealEstateInvestmentPropertyNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfMortgageLoans_53a01a41-c9a1-4a05-86dc-32891ffb04aa_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) on sale of residential loans</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfMortgageLoans_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfMortgageLoans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Sale of Mortgage Loans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfMortgageLoans" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnSaleOfMortgageLoans"/>
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    <link:label id="lab_us-gaap_RealEstateGrossAtCarryingValue_c85879fb-f79f-49b1-808c-74e9d0b53f93_totalLabel_en-US" xlink:label="lab_us-gaap_RealEstateGrossAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_RealEstateGrossAtCarryingValue_7e73fa8b-3b70-463b-9a60-e528b8587d21_periodStartLabel_en-US" xlink:label="lab_us-gaap_RealEstateGrossAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at beginning of period</link:label>
    <link:label id="lab_us-gaap_RealEstateGrossAtCarryingValue_7f6d2515-244f-4adc-a280-e3af92ce7bad_periodEndLabel_en-US" xlink:label="lab_us-gaap_RealEstateGrossAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at end of period</link:label>
    <link:label id="lab_us-gaap_RealEstateGrossAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_RealEstateGrossAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Gross</link:label>
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    <link:label id="lab_us-gaap_CreditDefaultSwapMember_d66f007b-d74f-4545-8387-fddb824bfa66_terseLabel_en-US" xlink:label="lab_us-gaap_CreditDefaultSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit default swaps</link:label>
    <link:label id="lab_us-gaap_CreditDefaultSwapMember_label_en-US" xlink:label="lab_us-gaap_CreditDefaultSwapMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Default Swap [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditDefaultSwapMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditDefaultSwapMember"/>
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    <link:label id="lab_stpr_GA_019c22f5-5bbb-7cde-9a30-7394dd6c7f77_terseLabel_en-US" xlink:label="lab_stpr_GA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Georgia</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_28efa695-cc36-4133-a07d-b50328bdab14_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_c1bc2458-5809-4762-87d9-79d7edfbf358_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award vesting period</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets_019c2ea4-17eb-72b8-831a-23778aef13ec_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesGoodwillAndIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and intangible assets</link:label>
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    <link:label id="lab_us-gaap_RealEstateImprovements_d9f1c63b-89db-455b-be2a-0efb7ee809aa_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateImprovements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Improvements</link:label>
    <link:label id="lab_us-gaap_RealEstateImprovements_label_en-US" xlink:label="lab_us-gaap_RealEstateImprovements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SEC Schedule, 12-28, Real Estate Companies, Investment in Real Estate, Improvements</link:label>
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    <link:label id="lab_us-gaap_CustomerRelationshipsMember_019bf84d-4f6a-75d8-8ae9-20e65c7b2af5_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
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    <link:label id="lab_stpr_FL_6f51712b-fc53-4bda-85f9-0049c6c1f745_terseLabel_en-US" xlink:label="lab_stpr_FL" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Florida</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_7ba9c208-50da-4584-907f-355ba3b51472_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
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    <link:label id="lab_adam_GainLossOnDeConsolidationOfJointVentureEquityInvestments_0996d4a7-e79a-4ece-a344-6020e8a1780e_terseLabel_en-US" xlink:label="lab_adam_GainLossOnDeConsolidationOfJointVentureEquityInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain on de-consolidation of joint venture equity investments in Consolidated VIEs</link:label>
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    <link:label id="lab_adam_ResidentialMortgageLoansHeldForSaleMember_019b9226-638e-7d3e-beb3-17290492d9a1_verboseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held for sale</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldForSaleMember_019be542-3b81-74bd-b121-f3fec17ba018_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Residential loans held for sale</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldForSaleMember_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans Held For Sale [Member]</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:to="lab_adam_ResidentialMortgageLoansHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_AgencyARMsMember_1f4f039a-c609-430c-8a42-16ed2b386153_terseLabel_en-US" xlink:label="lab_adam_AgencyARMsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustable rate</link:label>
    <link:label id="lab_adam_AgencyARMsMember_label_en-US" xlink:label="lab_adam_AgencyARMsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Agency ARMs [Member]</link:label>
    <link:label id="lab_adam_AgencyARMsMember_documentation_en-US" xlink:label="lab_adam_AgencyARMsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Agency ARMs.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_AgencyARMsMember" xlink:href="adam-20251231.xsd#adam_AgencyARMsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_AgencyARMsMember" xlink:to="lab_adam_AgencyARMsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_836249d4-c3b1-4758-bd04-83be8b1912b8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_30b7b853-f493-43f6-9f91-a86dc07a42f0_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities_8c3b9e56-d51a-4c35-9f93-1647377b90db_terseLabel_en-US" xlink:label="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contributions of non-controlling interest in Consolidated VIEs</link:label>
    <link:label id="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities_label_en-US" xlink:label="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contributions Of Non-controlling Interest In Consolidated Variable Interest Entities</link:label>
    <link:label id="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities_documentation_en-US" xlink:label="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contributions Of Non-controlling Interest In Consolidated Variable Interest Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:href="adam-20251231.xsd#adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:to="lab_adam_ContributionsOfNonControllingInterestInConsolidatedVariableInterestEntities" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs_3c545810-0ee8-4fa3-98ee-7b172b5f36a1_terseLabel_en-US" xlink:label="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in non-controlling interest related to de-consolidation of VIEs</link:label>
    <link:label id="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs_label_en-US" xlink:label="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Non-Controlling Interest Related to De-Consolidation of VIEs</link:label>
    <link:label id="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs_documentation_en-US" xlink:label="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Non-Controlling Interest Related to De-Consolidation of VIEs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:href="adam-20251231.xsd#adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:to="lab_adam_IncreaseDecreaseInNonControllingInterestRelatedToDeConsolidationOfVIEs" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RepaymentOfCollateralizedDebtResidential_b769c330-56fd-4383-9657-ba64accaa8c6_negatedLabel_en-US" xlink:label="lab_adam_RepaymentOfCollateralizedDebtResidential" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Payments made on and extinguishment of collateralized debt obligations</link:label>
    <link:label id="lab_adam_RepaymentOfCollateralizedDebtResidential_label_en-US" xlink:label="lab_adam_RepaymentOfCollateralizedDebtResidential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayment Of Collateralized Debt, Residential</link:label>
    <link:label id="lab_adam_RepaymentOfCollateralizedDebtResidential_documentation_en-US" xlink:label="lab_adam_RepaymentOfCollateralizedDebtResidential" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repayment Of Collateralized Debt, Residential</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RepaymentOfCollateralizedDebtResidential" xlink:href="adam-20251231.xsd#adam_RepaymentOfCollateralizedDebtResidential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RepaymentOfCollateralizedDebtResidential" xlink:to="lab_adam_RepaymentOfCollateralizedDebtResidential" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_019c2c96-eace-7a74-a074-93753fa02e82_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">GAAP/Tax differences</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesOther" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SingleFamilyEquityOwnershipInterestsMember_8c450ecb-a2f2-4601-8562-855634746468_terseLabel_en-US" xlink:label="lab_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Single-Family Equity Ownership Interest</link:label>
    <link:label id="lab_adam_SingleFamilyEquityOwnershipInterestsMember_label_en-US" xlink:label="lab_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Single-Family Equity Ownership Interests [Member]</link:label>
    <link:label id="lab_adam_SingleFamilyEquityOwnershipInterestsMember_documentation_en-US" xlink:label="lab_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Single-Family Equity Ownership Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:href="adam-20251231.xsd#adam_SingleFamilyEquityOwnershipInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:to="lab_adam_SingleFamilyEquityOwnershipInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet_fe26921a-0889-41f1-9bf6-8aafdf89b582_terseLabel_en-US" xlink:label="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses), net</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet_label_en-US" xlink:label="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Real Estate Mortgage Loans, Net</link:label>
    <link:label id="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet_documentation_en-US" xlink:label="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) On Real Estate Mortgage Loans, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:href="adam-20251231.xsd#adam_UnrealizedGainLossOnRealEstateMortgageLoansNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:to="lab_adam_UnrealizedGainLossOnRealEstateMortgageLoansNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_913f468c-1c99-49be-9989-cbc903736c7b_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities of disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MultiFamilyHeldForSaleMember_68e76e8d-198c-4693-9a11-219aab56bb55_terseLabel_en-US" xlink:label="lab_adam_MultiFamilyHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Multi-Family - Held for Sale</link:label>
    <link:label id="lab_adam_MultiFamilyHeldForSaleMember_label_en-US" xlink:label="lab_adam_MultiFamilyHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Multi Family Held For Sale [Member]</link:label>
    <link:label id="lab_adam_MultiFamilyHeldForSaleMember_documentation_en-US" xlink:label="lab_adam_MultiFamilyHeldForSaleMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Multi Family Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_MultiFamilyHeldForSaleMember" xlink:href="adam-20251231.xsd#adam_MultiFamilyHeldForSaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_MultiFamilyHeldForSaleMember" xlink:to="lab_adam_MultiFamilyHeldForSaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_a61da11b-8624-47cb-9588-32b3032fd2e8_totalLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total other income</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_72009102-341f-4d77-aaeb-de144c6aa83c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable_a54733cf-2a94-457a-bd0f-bfa119069609_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net payments made on mortgages payable on real estate</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable_cbd538a2-a660-4428-97b9-298a78f8b85a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net payments made on mortgages payable on real estate</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable_ef342da5-d8ea-40e3-8b42-aa9084de781a_negatedLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Total repayment of related mortgages payable</link:label>
    <link:label id="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable_label_en-US" xlink:label="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Repayments of) Notes Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromRepaymentsOfNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:to="lab_us-gaap_ProceedsFromRepaymentsOfNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SanAntonioTX1Member_9ebfbaa3-93fb-4dfc-8692-97d17ef7e75a_terseLabel_en-US" xlink:label="lab_adam_SanAntonioTX1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">San Antonio, TX</link:label>
    <link:label id="lab_adam_SanAntonioTX1Member_label_en-US" xlink:label="lab_adam_SanAntonioTX1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">San Antonio, TX 1 [Member]</link:label>
    <link:label id="lab_adam_SanAntonioTX1Member_documentation_en-US" xlink:label="lab_adam_SanAntonioTX1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">San Antonio, TX 1</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_347a43be-d3e3-4429-b71f-64ff0ac04cf9_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flows from Financing Activities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_019bf84d-4f6a-7e25-bf93-97870a24f35b_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net assets acquired</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less), and Goodwill</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale_019c22e9-374c-7bf5-a10d-f47a0e578732_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromCollectionOfLoansHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from repayments</link:label>
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    <link:label id="lab_adam_SwapMaturities2025Member_22121582-dde2-4945-8d84-7d3421366256_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
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    <link:label id="lab_us-gaap_VariableRateDomain_d14c9c8b-a6e5-49ef-b724-6d90ccb84a1b_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_6db09c63-61f3-4f11-982c-794fe739b409_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred revenue</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_84864e2a-7bad-4d96-8724-42d0522834a7_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
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    <link:label id="lab_adam_FinancingReceivableMeasurementInput_7e7d9be1-ef8a-4335-9aca-12a64bc8f481_terseLabel_en-US" xlink:label="lab_adam_FinancingReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loans receivable, measurement input</link:label>
    <link:label id="lab_adam_FinancingReceivableMeasurementInput_label_en-US" xlink:label="lab_adam_FinancingReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Measurement Input</link:label>
    <link:label id="lab_adam_FinancingReceivableMeasurementInput_documentation_en-US" xlink:label="lab_adam_FinancingReceivableMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financing Receivable, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancingReceivableMeasurementInput" xlink:href="adam-20251231.xsd#adam_FinancingReceivableMeasurementInput"/>
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    <link:label id="lab_us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1_5c0c822a-e4b3-45d4-818c-0daa0a36d99a_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal repayments received on residential loans</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Loan and Lease Originations and Principal Collections</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromLoanAndLeaseOriginationsAndPrincipalCollections1"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_6a56b147-de2f-4d5f-bdee-40a9918a19bd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Level 3 Assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
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    <link:label id="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral_61b47e54-e4bd-4f1a-81f1-3a278e8e476d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total derivative liabilities</link:label>
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    <link:label id="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate_0b61db1a-905e-4f21-8aed-fa24257f6787_terseLabel_en-US" xlink:label="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages payable on real estate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate" xlink:href="adam-20251231.xsd#adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate" xlink:to="lab_adam_DisposalGroupIncludingDiscontinuedOperationMortgagesPayableOnRealEstate" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock_019b920b-5d5c-7412-b609-abac5c02f952_terseLabel_en-US" xlink:label="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Repurchase Reserves for Origination Activity</link:label>
    <link:label id="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock_label_en-US" xlink:label="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repurchase Reserves For Origination Activity, Policy [Policy Text Block]</link:label>
    <link:label id="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Repurchase Reserves For Origination Activity, Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:href="adam-20251231.xsd#adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:to="lab_adam_RepurchaseReservesForOriginationActivityPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_63f969a2-7f29-40c5-a74b-6bfe0a61d499_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_fdd26182-992d-4909-9774-93e0c30ab4ea_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum shares issuable (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss_1d3b5988-5bcb-492c-ba28-f40aa6743709_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAccruedInterestAfterAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
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    <link:label id="lab_adam_SwapMaturities2028Member_92d1beb7-2e82-4bce-9c22-d5a3a25d4267_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment_f49bccb6-7900-4034-945a-f7fe6015eb60_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfRealEstateHeldforinvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of real estate held for investment</link:label>
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    <link:label id="lab_us-gaap_TransfersAndServicingAbstract_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfers and Servicing [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransfersAndServicingAbstract" xlink:to="lab_us-gaap_TransfersAndServicingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_d8032045-35db-4313-8d15-7543147d4d9c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, variable interest rate, type [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Variable Interest Rate, Type [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:to="lab_us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations_7f12b58f-3135-4710-9461-d4b91a617567_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated debentures, estimated fair value</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subordinated Debt Obligations, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisSubordinatedDebtObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_SunsetApartmentsPreferredLLCMember_96d5a379-7286-4a44-9b74-a924ff1200cc_terseLabel_en-US" xlink:label="lab_adam_SunsetApartmentsPreferredLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EHOF-NYMT Sunset Apartments Preferred, LLC</link:label>
    <link:label id="lab_adam_SunsetApartmentsPreferredLLCMember_label_en-US" xlink:label="lab_adam_SunsetApartmentsPreferredLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sunset Apartments Preferred, LLC [Member]</link:label>
    <link:label id="lab_adam_SunsetApartmentsPreferredLLCMember_documentation_en-US" xlink:label="lab_adam_SunsetApartmentsPreferredLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sunset Apartments Preferred, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_SunsetApartmentsPreferredLLCMember" xlink:href="adam-20251231.xsd#adam_SunsetApartmentsPreferredLLCMember"/>
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    <link:label id="lab_us-gaap_ReceivableTypeDomain_cece4a95-e9ff-4aae-a614-4c4632e4f0d7_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:label id="lab_us-gaap_ReceivableTypeDomain_label_en-US" xlink:label="lab_us-gaap_ReceivableTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableTypeDomain" xlink:to="lab_us-gaap_ReceivableTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_FinancialAssetForeclosureMember_a2a41f6d-544a-42be-901d-243fe50daf3c_terseLabel_en-US" xlink:label="lab_adam_FinancialAssetForeclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreclosure</link:label>
    <link:label id="lab_adam_FinancialAssetForeclosureMember_label_en-US" xlink:label="lab_adam_FinancialAssetForeclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Asset, Foreclosure [Member]</link:label>
    <link:label id="lab_adam_FinancialAssetForeclosureMember_documentation_en-US" xlink:label="lab_adam_FinancialAssetForeclosureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Financial Asset, Foreclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_FinancialAssetForeclosureMember" xlink:href="adam-20251231.xsd#adam_FinancialAssetForeclosureMember"/>
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    <link:label id="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities_f51ab0fe-ffa6-4804-9178-911d986af319_negatedTerseLabel_en-US" xlink:label="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Distributions</link:label>
    <link:label id="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities_label_en-US" xlink:label="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for Distributions to Redeemable Noncontrolling Interest in Variable Interest Entities</link:label>
    <link:label id="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities_documentation_en-US" xlink:label="lab_adam_PaymentForDistributionsToRedeemableNoncontrollingInterestInVariableInterestEntities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment for Distributions to Redeemable Noncontrolling Interest in Variable Interest Entities</link:label>
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    <link:label id="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget_6cbdc672-04f2-4850-b553-b9ccf375efaa_terseLabel_en-US" xlink:label="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vested shares target (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget" xlink:href="adam-20251231.xsd#adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget" xlink:to="lab_adam_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedTarget" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_MeasurementInputCollateralDefaultRateMember_7bed2689-236d-4d53-b7cd-ee0ec4c699c7_terseLabel_en-US" xlink:label="lab_adam_MeasurementInputCollateralDefaultRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral default rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferOfCertainFinancialAssetsAccountedForAsSecuredBorrowingsTable"/>
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    <link:label id="lab_us-gaap_DividendsPayableTable_cbd9078f-51fc-4bbc-bcf1-2cf3b047072f_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends Payable [Table]</link:label>
    <link:label id="lab_us-gaap_DividendsPayableTable_label_en-US" xlink:label="lab_us-gaap_DividendsPayableTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableTable" xlink:to="lab_us-gaap_DividendsPayableTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Revenue since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_efab5ddb-7bfc-4233-8030-27876571cc98_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average shares outstanding-basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_b9285fdd-fea6-4b8c-8e54-2fadd4e423ae_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic weighted average common shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_stpr_NJ_cabe08e5-7b6e-431d-b863-9e9f7689134f_terseLabel_en-US" xlink:label="lab_stpr_NJ" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Jersey</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_bd497ed5-de27-4334-adb8-573632d9747b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Computation of Basic and Dilutive Earnings (Loss) Per Common Share</link:label>
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    <link:label id="lab_srt_DirectorMember_0e552aab-c2ee-47f3-93ca-8d8a5036cd80_terseLabel_en-US" xlink:label="lab_srt_DirectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Director</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_DirectorMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_DirectorMember"/>
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    <link:label id="lab_us-gaap_TransferMortgagePayable_744bd574-2372-4264-a3ac-c4aa962becde_terseLabel_en-US" xlink:label="lab_us-gaap_TransferMortgagePayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Mortgages and notes payable assumed by purchaser of real estate held for sale in Consolidated VIEs</link:label>
    <link:label id="lab_us-gaap_TransferMortgagePayable_label_en-US" xlink:label="lab_us-gaap_TransferMortgagePayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transfer Mortgage Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferMortgagePayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferMortgagePayable"/>
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    <link:label id="lab_us-gaap_SubsequentEventsAbstract_0a46c82e-59d4-4922-a118-527007210755_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventsAbstract_label_en-US" xlink:label="lab_us-gaap_SubsequentEventsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Events [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SubsequentEventsAbstract"/>
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    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember_c3b01f3c-12ea-4f6d-8544-f1b1f214c249_terseLabel_en-US" xlink:label="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps, Credit Default Swaps, U.S. Treasury Futures</link:label>
    <link:label id="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember_label_en-US" xlink:label="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps, Credit Default Swaps, U.S. Treasury Futures [Member]</link:label>
    <link:label id="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember_documentation_en-US" xlink:label="lab_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Rate Swaps, Credit Default Swaps, U.S. Treasury Futures</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember" xlink:href="adam-20251231.xsd#adam_InterestRateSwapsCreditDefaultSwapsU.S.TreasuryFuturesMember"/>
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    <link:label id="lab_us-gaap_CostOfRevenue_1e03ed23-a9a6-4995-9b11-ac94d85fe4e0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CostOfRevenue" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Cost of real estate sales</link:label>
    <link:label id="lab_us-gaap_CostOfRevenue_label_en-US" xlink:label="lab_us-gaap_CostOfRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfRevenue" xlink:to="lab_us-gaap_CostOfRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_9474bd9c-5a10-4005-800b-140768a377f6_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease expense</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseExpense" xlink:to="lab_us-gaap_OperatingLeaseExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_31f0b1a4-dfd0-4f16-b205-24f8aeab30f2_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
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    <link:label id="lab_us-gaap_ShareBasedPaymentArrangementNonemployeeMember_3b4828c9-3a8b-4745-b0c3-ac4847e52860_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-employee director</link:label>
    <link:label id="lab_us-gaap_ShareBasedPaymentArrangementNonemployeeMember_label_en-US" xlink:label="lab_us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonemployee [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedPaymentArrangementNonemployeeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedPaymentArrangementNonemployeeMember"/>
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    <link:label id="lab_adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock_7ba69fba-132f-4bb5-805b-520d5f08e98a_terseLabel_en-US" xlink:label="lab_adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Preferred Equity and Mezzanine Loans, Fair Value Compared to Unpaid Principal</link:label>
    <link:label id="lab_adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock_label_en-US" xlink:label="lab_adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Equity and Mezzanine Loans, Fair Value Compared to Unpaid Principal [Table Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:href="adam-20251231.xsd#adam_PreferredEquityAndMezzanineLoansFairValueComparedToUnpaidPrincipalTableTextBlock"/>
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    <link:label id="lab_adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock_e9f43329-7518-4fa4-b1a3-c48d6ce9cdb3_terseLabel_en-US" xlink:label="lab_adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value Compared to Unpaid Principal</link:label>
    <link:label id="lab_adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock_label_en-US" xlink:label="lab_adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Residential Mortgage Loans, Fair Value Compared To Unpaid Principal [Table Text Block]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock" xlink:href="adam-20251231.xsd#adam_ResidentialMortgageLoansFairValueComparedToUnpaidPrincipalTableTextBlock"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_a84a07e4-12f8-42fd-97ba-6cc9e39ef229_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Realized Gains (Losses)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_d6429f79-cdba-40ed-a49b-bcefe3784ee0_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_ea6a458a-cf67-44c5-a7ca-35fadba6b468_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_339176c5-d6a6-406f-8f2d-a9d79695a85b_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_d9b29233-0ae3-49a7-8458-8752fee873ab_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems"/>
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    <link:label id="lab_adam_CollateralizedDebtObligationsAbstract_8c8e3263-99ad-4ca5-91fa-eea10967442d_terseLabel_en-US" xlink:label="lab_adam_CollateralizedDebtObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized debt obligations:</link:label>
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    <link:label id="lab_adam_CollateralizedDebtObligationsAbstract_documentation_en-US" xlink:label="lab_adam_CollateralizedDebtObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collateralized Debt Obligations</link:label>
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    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_012c0a75-f10b-4ac3-b074-ee08d74962df_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Impairment of real estate</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_e822b383-9edb-4680-94a7-84403e93925f_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of real estate</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_019c41b9-19f6-73dd-8848-1e4316fc33bd_verboseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Impairment of real estate in disposal group held for sale</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfRealEstate_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfRealEstate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Real Estate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfRealEstate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfRealEstate"/>
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    <link:label id="lab_adam_CommonStockTaxableDividendPerShareOrdinaryIncome_3260a390-3a65-478f-aaa4-f7b5a906a909_terseLabel_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShareOrdinaryIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock dividend per share, ordinary income (in dollars per share)</link:label>
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    <link:label id="lab_adam_CommonStockTaxableDividendPerShareOrdinaryIncome_documentation_en-US" xlink:label="lab_adam_CommonStockTaxableDividendPerShareOrdinaryIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Taxable Dividend Per Share, Ordinary Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_adam_CommonStockTaxableDividendPerShareOrdinaryIncome" xlink:href="adam-20251231.xsd#adam_CommonStockTaxableDividendPerShareOrdinaryIncome"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedGainLoss_2c1ab152-9fc4-4bf8-b7a8-96ae9bf326cf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gains (losses) on investments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleUnrealizedGainLoss"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements_d1d5e7e2-40c6-4068-bbaa-74546641ece5_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Paydowns/Distributions</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements"/>
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    <link:label id="lab_us-gaap_DerivativeAssetFairValueGrossLiability_9a1235ca-6ecf-49bf-b88c-3761d841bc51_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gross Amounts Offset in Balance Sheets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetFairValueGrossLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeAssetFairValueGrossLiability"/>
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    <link:label id="lab_us-gaap_SubsequentEventsTextBlock_1764e2ab-d9fa-4ac0-a82d-97c59f510a92_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsequent Events</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventsTextBlock" xlink:to="lab_us-gaap_SubsequentEventsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
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    <link:label id="lab_adam_IndianapolisINMember_10b0821f-37d4-4354-aefd-86479f094bc2_terseLabel_en-US" xlink:label="lab_adam_IndianapolisINMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indianapolis, IN</link:label>
    <link:label id="lab_adam_IndianapolisINMember_label_en-US" xlink:label="lab_adam_IndianapolisINMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indianapolis, IN [Member]</link:label>
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    <link:label id="lab_us-gaap_Liabilities_bb7e37cf-8863-4c22-b895-394a0a38af00_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/>
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    <link:label id="lab_adam_SwapMaturities2026Member_003da018-b237-4e4a-929a-3aa263deb6f8_terseLabel_en-US" xlink:label="lab_adam_SwapMaturities2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:label id="lab_us-gaap_SeriesGPreferredStockMember_cac2a692-516f-412e-8e10-72b92edf09ee_terseLabel_en-US" xlink:label="lab_us-gaap_SeriesGPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series G Preferred Stock</link:label>
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    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
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    <link:label id="lab_us-gaap_SecuritiesBorrowed_e02f3c29-cf83-4fa5-995b-426a38c344c1_terseLabel_en-US" xlink:label="lab_us-gaap_SecuritiesBorrowed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unencumbered investment securities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuritiesBorrowed" xlink:to="lab_us-gaap_SecuritiesBorrowed" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseOther"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_9c6664d3-c1e1-42ba-922b-e98497a33d67_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock issuance, net</link:label>
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    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_e59b0966-2421-404a-bf14-b3640fca5697_terseLabel_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ABS</link:label>
    <link:label id="lab_us-gaap_AssetBackedSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_AssetBackedSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset-Backed Securities [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetBackedSecuritiesMember" xlink:to="lab_us-gaap_AssetBackedSecuritiesMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_VariableRateAxis_007792f3-36af-4298-bca4-0951ec5f9d58_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
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    <link:label id="lab_adam_MortgageServicingRightsAdditionsAbstract_019be4fe-3f8a-7778-b6ae-92e10892ab39_terseLabel_en-US" xlink:label="lab_adam_MortgageServicingRightsAdditionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additions:</link:label>
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    <link:label id="lab_us-gaap_InterestExpenseSubordinatedNotesAndDebentures_8ef130cc-169f-48de-b0e2-e37a7f8c67a1_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseSubordinatedNotesAndDebentures" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subordinated debentures</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CounterpartyNameAxis"/>
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    <link:label id="lab_adam_ScheduleOfActivityOfResidentialLoansHeldForSaleTableTextBlock_019b0745-67ce-712b-969c-2b11bf08cc09_terseLabel_en-US" xlink:label="lab_adam_ScheduleOfActivityOfResidentialLoansHeldForSaleTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Activity of Residential Loans Held for Sale</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities_dbb287c7-a7b2-4c71-8e12-2e2dcbc94f61_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment securities available for sale:</link:label>
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    <link:label id="lab_adam_EmployeeMember_0f35de94-3533-4e73-87c1-ba4812dbec1b_terseLabel_en-US" xlink:label="lab_adam_EmployeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest_afe5bf4a-dc3c-460f-9e23-a1e41ac25616_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossIncludingPortionAttributableToNonredeemableNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income (loss) allocated to redeemable non-controlling interest</link:label>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_8b99fd44-8525-4c1c-a29a-231677261345_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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    <link:label id="lab_us-gaap_RealEstateIntercompanyProfitsIncludedInCarryingAmount_473f609a-7978-495d-9049-1b357670c90c_terseLabel_en-US" xlink:label="lab_us-gaap_RealEstateIntercompanyProfitsIncludedInCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount acquired from controlled and other affiliates</link:label>
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