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Leases - Narrative (Details) - DBMGi $ in Millions	Mar. 31, 2025 USD ($) installment	Dec. 31, 2024 USD ($)	May 01, 2024 USD ($) lease installment
Lessee, Lease, Description [Line Items]
Number of property leases with amended termination dates | lease			3
Early lease termination payment receivable | $	$ 4.0		$ 12.0
Surrender fees, number of equal installments to be received | installment			3
Surrender fees payments received for lease termination | $		$ 4.0
Surrender fees, number of equal installments to be received remaining | installment	2

X

- 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

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

X

- Definition

Early Lease Termination Payment Receivable

+ References

No definition available.

+ Details

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Namespace Prefix:	vate_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Number Of Property Leases With Amended Termination Dates

+ References

No definition available.

+ Details

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X

- Definition

Surrender Fees, Number Of Equal Installments To Be Received

+ References

No definition available.

+ Details

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Namespace Prefix:	vate_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

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- Definition

Surrender Fees, Number Of Equal Installments To Be Received, Remaining

+ References

No definition available.

+ Details

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Namespace Prefix:	vate_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Surrender Fees Payments Received For Termination Of Lease

+ References

No definition available.

+ Details

Name:	vate_SurrenderFeesPaymentsReceivedForTerminationOfLease
Namespace Prefix:	vate_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Details

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Namespace Prefix:
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Period Type: