Name:	fact_DeferredUnderwritingFeePayableNonCurrent
Namespace Prefix:	fact_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Market value percentage.

+ References

No definition available.

+ Details

Name:	fact_MarketValuePercentage
Namespace Prefix:	fact_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of trading days.

+ References

No definition available.

+ Details

Name:	fact_NumberOfTradingDays
Namespace Prefix:	fact_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Represent the number of units issued during period.

+ References

No definition available.

+ Details

Name:	fact_NumberOfUnitsIssuedDuringPeriod
Namespace Prefix:	fact_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of days in a redemption period.

+ References

No definition available.

+ Details

Name:	fact_RedemptionPeriod
Namespace Prefix:	fact_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Represents the underwriters option period from the date of Initial Public Offering.

+ References

No definition available.

+ Details

Name:	fact_UnderwritersOptionDay
Namespace Prefix:	fact_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share price of saleable stock paid or offered to be paid by acquirer in business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 40
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479299/805-40-55-10

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 42
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-42

+ Details

Name:	us-gaap_BusinessAcquisitionSharePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of equity in the acquiree held by the acquirer immediately before the acquisition date in a business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 38
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-38

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 48
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-48

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 25
-Paragraph 9
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479405/805-10-25-9

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-3

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

+ Details

Name:	us-gaap_BusinessCombinationStepAcquisitionEquityInterestInAcquireePercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

Reference 1: 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 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of warrants or rights outstanding.

+ References

No definition available.

+ Details

Name:	us-gaap_ClassOfWarrantOrRightOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Price of the entity's common stock which would be required to be attained for the conversion feature embedded in the debt instrument to become effective.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentConvertibleStockPriceTrigger
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
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

No definition available.

+ Details

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

- Definition

Price of a single share of a number of saleable stocks of a company.

+ References

No definition available.

+ Details

Name:	us-gaap_SharePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

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

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=fact_PublicWarrantMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=fact_PrivatePlacementWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=us-gaap_SeriesOfIndividuallyImmaterialBusinessAcquisitionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Commitments and Contingencies (Details) - USD ($)	6 Months Ended
Commitments and Contingencies (Details) - USD ($)	Jun. 30, 2025	Dec. 31, 2024	Nov. 27, 2024
Commitments and Contingencies [Line Items]
Underwriters option day	45 days
Cash underwriting discount per unit	$ 0.2
Cash underwriting discount (in Dollars)	$ 3,500,000
Deferred fee per unit	$ 0.4
Deferred fee payable (in Dollars)	$ 7,000,000	$ 7,000,000
Warrants outstanding (in Shares)	9,081,563	9,081,563
Number of trading days	10 days
Redemption period	30 days
Market value percentage	115.00%
Public Warrant [Member]
Commitments and Contingencies [Line Items]
Warrants outstanding (in Shares)	8,750,000
Price per warrant	$ 0.01
Market value percentage	180.00%
Redemption trigger price per share	$ 18
Private Placement Warrants [Member]
Commitments and Contingencies [Line Items]
Warrants outstanding (in Shares)	331,563
Business Combination [Member]
Commitments and Contingencies [Line Items]
Effective issued price per share	$ 9.2
Percentage of gross proceeds	60.00%
Business Combination [Member] \| Public Warrant [Member]
Commitments and Contingencies [Line Items]
Warrant expire term	5 years
Price per warrant	$ 9.2
Minimum [Member]
Commitments and Contingencies [Line Items]
Number of trading days	20 days
Maximum [Member]
Commitments and Contingencies [Line Items]
Number of trading days	30 days
Class A Ordinary Shares [Member]
Commitments and Contingencies [Line Items]
Price per warrant			$ 11.5
Number of trading days	20 days
Class A Ordinary Shares [Member] \| Public Warrant [Member]
Commitments and Contingencies [Line Items]
Price per share	$ 18
Over-Allotment Option [Member]
Commitments and Contingencies [Line Items]
Number of units issued (in Shares)	2,625,000