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Equity-Based Compensation - Additional Information (Details) - USD ($) $ / shares in Units, $ in Thousands | 1 Months Ended | 3 Months Ended | 9 Months Ended | 12 Months Ended |  |
--- | --- | --- | --- | --- | --- | ---
Jun. 30, 2023 | Jan. 31, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Dec. 31, 2023 | Mar. 31, 2023 | Dec. 31, 2022
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Capitalized amount of stock based compensation |  |  | $ 0 | $ 200 | $ 100 | $ 700 |  |  |
Weighted-average grant date fair value per option |  |  |  |  |  | $ 506.8 |  |  |
Awards granted, straight-line using third-party valuation (in dollars per share) |  |  |  |  |  |  |  | $ 243.2 | $ 1,200
Fair value of common stock for awards granted |  | $ 770.8 |  |  |  |  |  |  |
Restricted Stock |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Grants in period |  |  |  |  | 0 |  |  |  |
Stock Appreciation Rights (SARs) |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Grants in period |  |  |  |  | 0 |  |  |  |
2020 Equity Incentive Plan [Member] | Software Costs |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Capitalized amount of stock based compensation |  |  |  | 200 |  | $ 700 |  |  |
2023 & 2020 Equity Incentive Plan [Member] |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Capitalized amount of stock based compensation |  |  | 3,200 | 9,600 | $ 5,000 | 24,500 |  |  |
Number of options, Granted | 32,375 |  |  |  | 0 |  |  |  |
Number of accelerated vested shares |  | 148 |  |  |  |  |  |  |
Number of repriced option awards |  | 7,538 |  |  |  |  |  |  |
Recognized stock compensation expense |  |  | 3,157 | $ 4,836 | $ 9,448 | $ 23,773 |  |  |
Unrecognized stock-based compensation expense |  |  | 7,500 |  | $ 7,500 |  | $ 17,100 |  |
Additional Expense |  | $ 500 |  |  |  |  |  |  |
Weighted-average period expected to be recognized |  |  |  |  | 1 year |  | 1 year 8 months 12 days |  |
2023 & 2020 Equity Incentive Plan [Member] | Employee Stock Option |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Number of options, Granted |  |  |  |  | 0 |  |  |  |
2023 Equity Incentive Plan [Member] | Software Costs |  |  |  |  |  |  |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Capitalized amount of stock based compensation |  |  | $ 0 |  | $ 100 |  |  |  |

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