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Stock Based Compensation - Additional Information (Details) - USD ($)
3 Months Ended 12 Months Ended
Oct. 02, 2024
Sep. 20, 2024
Apr. 04, 2019
Dec. 31, 2024
Dec. 31, 2024
Oct. 01, 2024
Dec. 31, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Description of forward stock split   103-for-one forward stock split     103-for-one stock split    
Common stock, shares, issued       334,461,630 334,461,630   281,211,630
Common stock, shares, outstanding       334,461,630 334,461,630   281,211,630
Aggregate intrinsic value of stock options outstanding       $ 6,600,000 $ 6,600,000    
Aggregate intrinsic value of stock options exercisable         700,000    
Shares, vested 0            
Compensation expense       17,400,000      
Unrecognized compensation costs       $ 22,800,000 22,800,000    
Stock compensation         $ 17,376,000    
Maximum              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued, exercise of incentive stock options         19,662,698    
2019 Long-Term Incentive Plan ("Prior Plan")              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued         0    
Percentage of time based RSAs and options vested subject to continued employment         50.00%    
Percentage of performance based RSAs and options vested subject to continued employment         50.00%    
Percentage of discount applied for lack of marketability associated     30.00%        
2024 Incentive Award Plan              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued 19,662,698            
Employee Stock Purchase Plan (ESPP)              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Common stock, shares, outstanding       334,461,630 334,461,630    
Dynasty Parent Holdings, L.P.              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Common stock, shares, issued   281,211,630          
Common stock, shares, outstanding   281,211,630          
Dynasty Parent Holdings, L.P. | Class A-1 Units and Class A-2 Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   275,053,375          
Dynasty Parent Holdings, L.P. | Class B Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   6,158,255          
Restricted Stock Awards (RSA) | Employee Stock Purchase Plan (ESPP)              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Common stock, shares, outstanding       6,036,550 6,036,550    
Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P. | Class A-1 Units and Class A-2 Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   8,157          
Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P. | Class B Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   6,028,394          
IPO              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Price per share           $ 24  
Compensation expense $ 0            
IPO | Dynasty Parent Holdings, L.P.              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Price per share   $ 24          
IPO | Dynasty Parent Holdings, L.P. | Class A-1 Units and Class A-2 Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   275,053,375          
IPO | Dynasty Parent Holdings, L.P. | Class B Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   6,158,255          
IPO | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P. | Class A-1 Units and Class A-2 Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   8,157          
IPO | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P. | Class B Units              
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]              
Shares issued   6,028,394