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Nature of Operations and Basis of Presentation - Additional Information (Details) - USD ($)
$ / shares in Units, $ in Millions
 12 Months Ended
Oct. 01, 2024
Sep. 20, 2024
Dec. 31, 2024
Sep. 19, 2024
Dec. 31, 2023
Class of Stock [Line Items]          
Common stock, voting shares authorized   3,500,000,000 3,500,000,000 5,000,000 3,500,000,000
Common stock, non-voting shares authorized   70,000,000   100,000  
Description of forward stock split   103-for-one forward stock split 103-for-one stock split    
Common stock, shares, issued     334,461,630   281,211,630
Common stock, shares, outstanding     334,461,630   281,211,630
Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Common stock, shares, issued   281,211,630      
Common stock, shares, outstanding   281,211,630      
Class A-1 Units and Class A-2 Units | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   275,053,375      
Class A-1 Units and Class A-2 Units | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   8,157      
Class B Units | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   6,158,255      
Class B Units | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   6,028,394      
IPO          
Class of Stock [Line Items]          
Price per share $ 24        
Number of share issued 69,000,000        
Shares issued to exercise of underwriters option to purchase additional shares 9,000,000        
Proceeds from issue of shares $ 1,202.8        
Underwriting discounts and commissions 67.1        
Estimated offering expenses $ 8.1        
IPO | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Price per share   $ 24      
IPO | Class A-1 Units and Class A-2 Units | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   275,053,375      
IPO | Class A-1 Units and Class A-2 Units | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   8,157      
IPO | Class B Units | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   6,158,255      
IPO | Class B Units | Restricted Stock Awards (RSA) | Dynasty Parent Holdings, L.P.          
Class of Stock [Line Items]          
Shares issued   6,028,394      
IPO | Company          
Class of Stock [Line Items]          
Number of share issued 53,250,000        
IPO | Existing Stockholders          
Class of Stock [Line Items]          
Number of share issued 15,750,000