Face (par) amount of debt instrument at time of issuance.

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

- Definition

Effective interest rate for the funds borrowed under the debt agreement considering interest compounding and original issue discount or premium.

+ References

+ Details

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

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
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/exampleRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482949/835-30-55-8

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(f))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69B

Reference 6: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69C

Reference 7: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69E
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69E

Reference 8: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69F
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69F

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 11: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (h)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 15: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 16: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 17: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 18: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 19: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 20: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 21: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 22: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 23: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 24: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 25: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1I
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1I

Reference 26: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-2

Reference 27: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482900/835-30-50-1

+ Details

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

- Definition

Amount of the cost of borrowed funds accounted for as interest expense for debt.

+ 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(8))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69E
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69E

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69F
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69F

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-6

+ Details

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

- Definition

Amount of cash paid for interest, excluding capitalized interest, classified as operating activity. Includes, but is not limited to, payment to settle zero-coupon bond for accreted interest of debt discount and debt instrument with insignificant coupon interest rate in relation to effective interest rate of borrowing attributable to accreted interest of debt discount.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 17
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-17

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 25
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-25

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-2

+ Details

Name:	us-gaap_InterestPaidNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of interest payable on debt, including, but not limited to, trade payables.

+ 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)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 2: 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)(15)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

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

- Definition

The cash outflow for debt initially having maturity due after one year or beyond the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 15
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-15

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-03(i)(2))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479886/946-10-S99-3

+ Details

Name:	us-gaap_RepaymentsOfLongTermDebt
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Debt Covenant, Mandatory Prepayment, Proceeds From Certain Asset Sales, Amount Threshold

+ References

No definition available.

+ Details

Name:	vate_DebtCovenantMandatoryPrepaymentProceedsFromCertainAssetSalesAmountThreshold
Namespace Prefix:	vate_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Debt Covenant, Mandatory Prepayment, Proceeds from Equity Sales Percentage

+ References

No definition available.

+ Details

Name:	vate_DebtCovenantMandatoryPrepaymentProceedsFromEquitySalesPercentage
Namespace Prefix:	vate_
Data Type:	dtr-types1:percentItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=vate_NonOperatingCorporateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SecuredDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=vate_SeniorNotesDue2026850Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=vate_CGICMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_CounterpartyNameAxis=vate_DBMGiMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_StatementScenarioAxis=srt_ScenarioForecastMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Debt Obligations - Non-Operating Corporate CGIC Unsecured Notes Due 2026 Narrative (Details) - USD ($)		3 Months Ended
	Apr. 26, 2024	Mar. 31, 2025	Mar. 31, 2024	May 08, 2025	Dec. 31, 2024	May 09, 2024	May 08, 2024	May 09, 2023	Dec. 31, 2021	Feb. 01, 2021
Debt Instrument [Line Items]
Cash paid for interest		$ 19,500,000	$ 19,600,000
Accrued interest and exit fees (current portion)		$ 64,300,000			$ 61,000,000.0
Non-Operating Corporate \| Secured Debt \| 8.50% Senior Secured Notes due 2026
Debt Instrument [Line Items]
Face amount									$ 330,000,000
Interest rate		8.50%							8.50%	8.50%
Interest rate, effective percentage									9.30%
CGIC \| Non-Operating Corporate \| Secured Debt
Debt Instrument [Line Items]
Face amount								$ 35,100,000
Repayments of long-term debt	$ 4,100,000
CGIC \| Non-Operating Corporate \| Secured Debt \| 8.50% Senior Secured Notes due 2026
Debt Instrument [Line Items]
Interest cost relating to contractual interest coupon		$ 1,400,000	1,600,000
Cash paid for interest		1,200,000	$ 800,000
Accrued interest and exit fees (current portion)		$ 3,600,000			$ 3,400,000
DBMGi \| Non-Operating Corporate
Debt Instrument [Line Items]
Interest rate						16.00%	9.00%
Interest rate, effective percentage		17.50%			17.50%
Debt covenant, mandatory prepayment, proceeds from certain asset sales, amount threshold		$ 3,000,000
Debt covenant, mandatory prepayment, proceeds from equity sales percentage		12.50%
DBMGi \| Non-Operating Corporate \| Forecast
Debt Instrument [Line Items]
Interest rate				32.00%