Related Party Transactions (Details) - USD ($)	12 Months Ended
Dec. 31, 2025	Dec. 31, 2024
Related Party Transactions
Total other liabilities	$ 6,533,000	$ 13,466,000
Total LHFS at fair value	466,681,000	399,241,000
General and administrative	45,323,000	52,230,000
Share-based payment arrangement, expense	20,432,000	26,753,000
Technology Integration and License Agreement \| Related party
Related Party Transactions
Total other liabilities	100,000	100,000
Master Loan Purchase Agreement \| Related party
Related Party Transactions
Total LHFS at fair value	2,500,000	4,200,000
Master Loan Purchase Agreement \| Related party \| Better Trust I
Related Party Transactions
Master loan purchase agreement, amount	20,000,000.0
RSU Grants \| Related party
Related Party Transactions
Share-based payment arrangement, expense	700,000
Mortgage platform \| Technology Integration and License Agreement \| Related party
Related Party Transactions
Expenses	900,000	1,000,000.0
Mortgage platform \| Data Analytics Services Agreement \| Related party
Related Party Transactions
General and administrative	0	100,000
Mortgage platform \| Data Analytics Services Agreement \| Related party \| Accounts Payable and Accrued Liabilities
Related Party Transactions
Total other liabilities	$ 0	$ 0

Master Loan Purchase Agreement, Amount

No definition available.

Name:	aurcu_MasterLoanPurchaseAgreementAmount
Namespace Prefix:	aurcu_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479983/718-10-S45-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479830/718-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_AllocatedShareBasedCompensationExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The aggregate costs related to goods produced and sold and services rendered by an entity during the reporting period. This excludes costs incurred during the reporting period related to financial services rendered and other revenue generating activities.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-4A

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476153/220-40-55-11

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 55
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476153/220-40-55-4

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(2)(d))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(2)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 924
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 11.L)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479941/924-10-S99-1

Reference 7: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476148/220-40-50-6

+ Details

Name:	us-gaap_CostOfGoodsAndServicesSold
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The aggregate total of expenses of managing and administering the affairs of an entity, including affiliates of the reporting entity, which are not directly or indirectly associated with the manufacture, sale or creation of a product or product line.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

+ Details

Name:	us-gaap_GeneralAndAdministrativeExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Fair value portion of mortgage loans held-for-sale.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-28

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-11

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-10

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_MortgagesHeldForSaleFairValueDisclosure
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of liabilities classified as other.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 480
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 64
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481620/480-10-55-64

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-14

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-11

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(15))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

Reference 6: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 830
-Name Accounting Standards Codification
-Section 55
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479168/946-830-55-12

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(12)(b)(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(12)(b)(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 9: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(12)(b)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 10: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(17))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

Name:	us-gaap_OtherLiabilities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 850
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483326/850-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 850
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483326/850-10-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 850
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483326/850-10-50-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(k)(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(k)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-13

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(i))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(ii))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(g)(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

+ Details

Name:	us-gaap_RelatedPartyTransactionLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=aurcu_TechnologyIntegrationAndLicenseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=us-gaap_RelatedPartyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=aurcu_MasterLoanPurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	dei_LegalEntityAxis=aurcu_BetterTrustIMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=aurcu_RSUGrantsForConsultingServicesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=aurcu_MortgagePlatformMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=aurcu_DataAnalyticsServicesAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BalanceSheetLocationAxis=us-gaap_AccountsPayableAndAccruedLiabilitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: