Amount of interest expense on finance lease liability.

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-4

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount of amortization expense attributable to right-of-use asset from finance lease.

+ References

+ Details

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

- Definition

Amount of lease cost recognized by lessee for lease contract.

+ References

+ Details

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

- 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 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-7A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-3

+ Details

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

- Definition

Amount of single lease cost, calculated by allocation of remaining cost of lease over remaining lease term. Includes, but is not limited to, single lease cost, after impairment of right-of-use asset, calculated by amortization of remaining right-of-use asset and accretion of lease liability.

+ References

+ Details

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

- Definition

Amount of short-term lease cost, excluding expense for lease with term of one month or less.

+ References

+ Details

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

- Details

Name:	us-gaap_FreshStartAdjustmentsTypeOfFreshStartAdjustmentAxis=pal_SuccessorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FreshStartAdjustmentsTypeOfFreshStartAdjustmentAxis=pal_PredecessorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Leases - Schedule of Lease Cost (Details) - USD ($)	4 Months Ended	12 Months Ended
Leases - Schedule of Lease Cost (Details) - USD ($)	May 12, 2024	Dec. 31, 2025	Dec. 31, 2024	Dec. 31, 2023
Successor [Member]
Schedule of Lease Cost [Line Items]
Operating lease cost		$ 2,729,053	$ 1,506,424
Finance lease costs:
Amortization of finance lease assets		89,184	20,671
Interest on lease liabilities		6,950	3,362
Short-term lease costs		474,552	577,265
Total lease costs		$ 3,299,739	$ 2,107,722
Predecessor [Member]
Schedule of Lease Cost [Line Items]
Operating lease cost	$ 27,951			$ 28,918
Finance lease costs:
Amortization of finance lease assets	160,032			483,731
Interest on lease liabilities	132,062			201,072
Short-term lease costs	99,533			145,923
Total lease costs	$ 419,578			$ 859,644