Tax Receivable Agreement and Income Taxes - Additional Information (Details) - USD ($)		1 Months Ended		3 Months Ended			9 Months Ended		12 Months Ended
	Jan. 01, 2023	Dec. 31, 2023	Aug. 31, 2022	Sep. 30, 2024	Dec. 31, 2023	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Dec. 31, 2022
Subsidiary, Sale of Stock [Line Items]
Percentage of net cash saving to be paid							85.00%		85.00%
Percentage of net cash saving to be retained							15.00%		15.00%
Total TRA liability recognized		$ 5,242,000		$ 41,000	$ 5,242,000		$ 41,000		$ 5,242,000	$ 4,333,000
Outside basis difference in partnership							0		6,100,000
Deferred tax assets, valuation allowance		500,000		7,300,000	$ 500,000		7,300,000		500,000	0
Aggregate payment on tax receivable agreement							0	$ 100,000
Derecognition of tax receivable agreement liability				$ 5,201,000		$ 0	$ 5,201,000	$ 0
Corporation income tax rate (in percent)	20.45%			2884.70%	23.35%	4.70%	(85.10%)	4.90%
Operating loss carryforwards		1,100,000			$ 1,100,000				1,100,000
Uncertain tax positions		$ 0		$ 0	$ 0		$ 0		$ 0	$ 0
Domestic Tax Jurisdiction
Subsidiary, Sale of Stock [Line Items]
Operating loss carryforwards				$ 4,400,000			$ 4,400,000
Class A Common Stock | DDM
Subsidiary, Sale of Stock [Line Items]
Number of units exchanged (in shares)		410,000	100,000						410,000	100,000