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Summary of Significant Accounting Policies (Details) - USD ($)		3 Months Ended		9 Months Ended		12 Months Ended
	Jan. 18, 2023	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2024	Sep. 30, 2023	Dec. 31, 2023	Dec. 31, 2022
Summary of Significant Accounting Policies [Line Items]
Allowance for credit losses		$ 3,145,168		$ 3,145,168		$ 862,580
Write-offs		$ 0		0
Additionally write-offs				$ 2,282,588	$ 967,148
Basic loss per share (in Dollars per share)		$ 0.3		$ 0.3
Diluted loss per share (in Dollars per share)		$ 0.49		$ 0.49
Insured limits		$ 4,080,061		$ 4,080,061		6,979,011
Inventory		482,251		$ 482,251		350,353
Common units issued (in Shares)				33,730,000
Percentage of business combination				24.167%
Uncertain tax positions		$ 0		$ 0		0
Unrecognized tax benefits
Effective tax rate		1.50%	0.00%	2.70%	0.00%
Cash savings percentage				85.00%
Total unrecorded TRA liability		$ 48,800,000		$ 48,800,000
Cash equivalents
Ordinary shares (in Shares)						27,840,000
Accumulated deficit						$ 3,066,977	3,986,568
Redemption value	$ 255,875,758
Deposited in the Trust Account						1,116,710
Payment of interest and penalties
OpCo, LLC [Member]
Summary of Significant Accounting Policies [Line Items]
Percentage of business combination				87.00%
Maximum [Member]
Summary of Significant Accounting Policies [Line Items]
Additionally write-offs		1,820,365		$ 1,820,365
Minimum [Member]
Summary of Significant Accounting Policies [Line Items]
Additionally write-offs		$ 1,820,365		$ 1,820,365
Customer [Member]
Summary of Significant Accounting Policies [Line Items]
Recoveries			$ 0		$ 0
Redeemable Noncontrolling Interests [Member]
Summary of Significant Accounting Policies [Line Items]
Percentage of business combination				13.00%
Class A Ordinary Shares Subject To Possible Redemption [Member]
Summary of Significant Accounting Policies [Line Items]
Redemption value						272,554,813
Income Taxes Benefits [Member]
Summary of Significant Accounting Policies [Line Items]
Unrecognized tax benefits

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