Fair Value Measurements (Tables)

3 Months Ended

12 Months Ended

Mar. 31, 2023

Dec. 31, 2022

Statement [Line Items]

Schedule of quantitative information regarding Level 3 fair value measurements inputs

	March 31, 2023		March 30, 2023
Risk-free interest rate	3.70	%	3.80	%
Expected volatility	40	%	40	%
Expected dividend yield	—	%	—	%

Schedule of change in the derivative fair value of the warrant liabilities

			Derivative
			private		Derivative
	Contingent		placement		stock
	earnout		warrant		option
	liability		liability		liability
Liability at January 1, 2023	$	—	$	—	$	—
Recognition		242,211,404		625,370		1,189,685
Forfeitures		—		(890,001)		—
Change in fair value		203,418,892		1,213,963		922,263
Liability at March 31, 2023	$	445,630,296	$	949,332	$	2,111,948

DiamondHead Holdings Corp.

Statement [Line Items]

Schedule of company's financial assets and liabilities that are measured at fair value on a recurring basis

	Fair Value Measured as of December 31, 2022
	Level 1		Level 2		Level 3		Total
Assets:
Investments held in Trust Account – Money Market Funds	$	349,152,086	$	—	$	—	$	349,152,086
Liabilities:
Derivative public warrant liabilities	$	905,630	$	—	$	—	$	905,630
Derivative private warrant liabilities	$	—	$	—	$	625,370	$	625,370

	Fair Value Measured as of December 31, 2021
	Level 1		Level 2		Level 3		Total
Assets
Investments held in Trust Account – Money Market Funds	$	345,020,717	$	—	$	—	$	345,020,717
Liabilities:
Derivative public warrant liabilities	$	5,175,000	$	—	$	—	$	5,175,000
Derivative private warrant liabilities	$	—	$	—	$	3,619,330	$	3,619,330

Schedule of quantitative information regarding Level 3 fair value measurements inputs

	As of December 31,			As of December 31,
	2022			2021
Exercise price	$	11.50		$	11.50
Stock Price	$	10.05		$	9.74
Option term (in years)		5.00			4.82
Volatility		40	%		12	%
Risk-free interest rate		4.1	%		1.3	%

Schedule of change in the derivative fair value of the warrant liabilities

Derivative warrant liabilities at January 1, 2022 – Level 3	$	3,619,330
Change in fair value of derivative warrant liabilities – Level 3		(2,993,960)
Derivative warrant liabilities at December 31, 2022 – Level 3	$	625,370

Derivative warrant liabilities at January 1, 2021 – Level 3	$	—
Issuance of Derivative Warrants – Level 3		13,161,830
Transfer of Public Warrants to Level 1		(7,762,500)
Change in fair value of derivative warrant liabilities – Level 3		(1,780,000)
Derivative warrant liabilities at December 31, 2021 – Level 3	$	3,619,330