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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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