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Equity-Based Compensation - Additional Information (Details) - USD ($)
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
Dec. 31, 2022
Mar. 31, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Capitalized amount of stock based compensation     $ 0 $ 200,000 $ 100,000 $ 700,000 $ 900,000 $ 0  
Weighted-average grant date fair value per option         $ 50,680   $ 46,520 $ 108,680  
Awards granted, straight-line using third-party valuation (in dollars per share)               $ 120,000 $ 24,320
Fair value of common stock for awards granted   $ 77,080              
Restricted Stock                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Grants in period         0   0    
Stock Appreciation Rights (SARs)                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Grants in period         0   0    
2023 and 2020 Equity Incentive Plan [Member]                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Capitalized amount of stock based compensation     3,200,000 9,600,000 $ 5,000,000 24,500,000 $ 900 $ 0  
Number of options, Granted 324       0   938    
Number of accelerated vested shares   1              
Number of repriced option awards   75              
Recognized stock compensation expense     3,157,000 4,836,000 $ 9,448,000 23,773,000 $ 29,943,000 6,348,000  
Unrecognized stock-based compensation expense     7,500,000   $ 7,500,000   $ 17,100,000 $ 5,900,000  
Additional Expense   $ 500,000              
Weighted-average period expected to be recognized         1 year   1 year 8 months 12 days 1 year 7 months 6 days  
2023 and 2020 Equity Incentive Plan [Member] | Stock Option                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Number of options, Granted         0   938    
2023 and 2020 Equity Incentive Plan [Member] | Previously Reported [Member]                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Number of accelerated vested shares   2              
2023 and 2020 Equity Incentive Plan [Member] | Software Costs                  
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]                  
Capitalized amount of stock based compensation     $ 0 $ 200,000 $ 100,000 $ 700,000