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Fair Value Measurements (Tables)

6 Months Ended

12 Months Ended

Jun. 30, 2024

Dec. 31, 2023

Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]

Schedule of Assets Measured at Fair Value on a Recurring Basis

The following table presents information about the Company’s assets and liabilities that are measured at fair value on a recurring basis at June 30, 2024 (Successor), and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value:

(dollars in thousands)		Public Warrants (Level 1)				Senior Secured Term Loan (Level 2)				Private Placement Warrants (Level 3)				Working Capital Warrants (Level 3)				Total Liabilities Fair Value
Fair value as of February 14, 2024 (Successor)		$	39,962			$	761,401			$	19,813			$	—			$	821,176
Additions			—				9,801				—				10,283				20,084
Change in valuation inputs or other assumptions			(2,875	)			—				550				562				(1,763	)
Fair Value as of March 31, 2024 (Successor)			37,087				771,202				20,363				10,845				839,497
Additions			—				19,175				—				—				19,175
Change in valuation inputs or other assumptions			24,294				—				37,839				19,045				81,178
Fair value as of June 30, 2024 (Successor)		$	61,381			$	790,377			$	58,202			$	29,890			$	939,850

Summary of Level 3 Inputs to Determine Fair Value

The following table provides quantitative information regarding Level 3 inputs used to determine the fair values of Private Placement Warrants held by FL Co-Investment and Intrepid Financial Partners as of June 30, 2024 (Successor).

Inputs		June 30, 2024 (Successor)
Stock price		$	15.07
Strike price		$	11.50
Term (in years)			1.65
Volatility			45.0	%
Risk-free rate			4.73	%
Dividend yield			0.00	%

The following table provides quantitative information regarding Level 3 fair value measurements used to determine the fair value of the Working Capital Warrants and the Private Placement Warrants, excluding Private Placement Warrants held by FL Co-Investment and Intrepid Financial Partners, as of June 30, 2024 (Successor).

Inputs		June 30, 2024 (Successor)
Stock price		$	15.07
Strike price		$	11.50
Term (in years)			4.63
Volatility			60.0	%
Risk-free rate			4.27	%
Dividend yield			0.00	%

Flame Acquisition Corp [Member]

Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]

Schedule of Assets Measured at Fair Value on a Recurring Basis

The following table presents information about the Company’s assets and liabilities that are measured at fair value on a recurring basis at December 31, 2023 and 2022, and indicates the fair value hierarchy of the valuation inputs the Company utilized to determine such fair value:

Description:		Level				December 31, 2023				Level				December 31, 2022
Assets:
Funds held in Trust Account			1			$	—				1			$	290,718,297
Liabilities:
Warrant liability—Public Warrants			1			$	27,743,750				1			$	9,343,750
Warrant liability—Private Placement Warrants			3			$	11,470,000				3			$	2,805,500
Convertible Promissory Notes—Related Parties			3			$	6,381,294				3			$	1,409,730

Summary of Level 3 Inputs to Determine Fair Value

The following table provides quantitative information regarding Level 3 fair value measurements used to determine the fair value of the Private Placement Warrants, excluding Private Placement Warrants held by FL Co-Investment and Intrepid Financial Partners, as of December 31, 2023 and 2022.

Inputs		December 31, 2023				December 31, 2022
Stock price		$	11.39			$	10.05
Strike price		$	11.50			$	11.50
Term (in years)			5.09				5.25
Volatility			5.3	%			0.0	%
Risk-free rate			3.77	%			3.91	%
Dividend yield			0.00	%			0.00	%

Schedule of Changes in the Fair Value of Warrant Liabilities

The following table presents the changes in the fair value of warrant liabilities:

		Public				Private Placement				Warrant Liabilities
Fair value as of December 31, 2021		$	8,625,000			$	4,022,250			$	12,647,250
Change in valuation inputs or other assumptions			718,750				(1,216,750	)			(498,000	)
Fair value as of December 31, 2022			9,343,750				2,805,500				12,149,250
Change in valuation inputs or other assumptions			18,400,000				8,664,500				27,064,500
Fair value as of December 31, 2023		$	27,743,750			$	11,470,000			$	39,213,750

Promissory Note [Member] | Flame Acquisition Corp [Member]

Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]

Summary of Level 3 Inputs to Determine Fair Value

The convertible promissory notes were valued using a combination of Black-Scholes and Geske models, which is considered to be primarily a Level 3 fair value measurement input. The estimated fair value of the Promissory Notes was based on the following significant inputs:

Inputs		2023 Input (a)				December 31, 2023				December 31, 2022
Exercise price			$      11.50			$	11.50			$	11.50
Volatility			1.9% - 2.5	%			11.4	%			1.2	%
Expected term to warrant expiration			5.2 - 5.6 years				5.1 years				5.3 years
Risk-free-rate			3.39% - 4.17	%			3.77	%			3.91	%
Dividend yield			0	%			0	%			0	%
Stock price			$ 10.13 - $10.39			$	11.39			$	10.05

(a) Represents the range of inputs utilized on the respective dates of the initial valuations of the various convertible note draws and extinguishments during the year ended December 31, 2023.

Schedule of Changes in the Fair Value of Warrant Liabilities

The following table presents the changes in the fair value of the Level 3 Promissory Notes:

Fair value as of December 31, 2021		$	956,115
Proceeds received through Convertible Promissory Note on March 29, 2022			335,000
Initial measurement of fair value of Promissory Note			(52,126	)
Change in fair value of Promissory Notes			170,741
Fair value as of December 31, 2022		$	1,409,730
Principal amount of Promissory Notes amended on March 29, 2023			726,370
Initial measurement of fair value of Promissory Notes upon extinguishment of debt			(42,205	)
Proceeds received through Convertible Promissory Notes on May 12, 2023, June 28, 2023, and August 30, 2023			1,080,000
Initial Measurement of fair value of Promissory Notes			(490,995	)
Change in valuation inputs or other assumptions			3,698,394
Fair value as of December 31, 2023		$	6,381,294

Other Private Placement Warrants [Member] | Flame Acquisition Corp [Member]

Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]

Summary of Level 3 Inputs to Determine Fair Value

The following table provides quantitative information regarding Level 3 inputs used to determine the fair values of Private Placement Warrants as of December 31, 2023 and 2022.

		December 31, 2023				December 31, 2022
Stock price		$	11.39			$	10.05
Strike price		$	11.50			$	11.50
Term (in years)			2.15				3.15
Volatility			5.3	%			0.0	%
Risk-free rate			4.11	%			4.12	%
Dividend yield			0.00	%			0.00	%

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- Definition

Tabular disclosure of input and valuation technique used to measure fair value and change in valuation approach and technique for each separate class of asset and liability measured on recurring and nonrecurring basis.

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Tabular disclosure of the fair value measurement of liabilities using significant unobservable inputs (Level 3), a reconciliation of the beginning and ending balances, separately presenting changes attributable to the following: (1) total gains or losses for the period (realized and unrealized), segregating those gains or losses included in earnings (or changes in net assets), and gains or losses recognized in other comprehensive income (loss) and a description of where those gains or losses included in earnings (or changes in net assets) are reported in the statement of income (or activities); (2) purchases, sales, issues, and settlements (each type disclosed separately); and (3) transfers in and transfers out of Level 3 (for example, transfers due to changes in the observability of significant inputs) by class of liability.

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Tabular disclosure of assets and liabilities, including [financial] instruments measured at fair value that are classified in stockholders' equity, if any, that are measured at fair value on a recurring basis. The disclosures contemplated herein include the fair value measurements at the reporting date by the level within the fair value hierarchy in which the fair value measurements in their entirety fall, segregating fair value measurements using quoted prices in active markets for identical assets (Level 1), significant other observable inputs (Level 2), and significant unobservable inputs (Level 3).

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