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Nature of Operations and Basis of Presentation - Additional Information (Details) - USD ($)
$ / shares in Units, $ in Millions
 3 Months Ended
Oct. 02, 2025
Mar. 26, 2025
Oct. 02, 2024
Sep. 20, 2024
Mar. 31, 2025
Dec. 31, 2024
Sep. 19, 2024
Class of Stock [Line Items]              
Common stock, voting shares authorized       3,500,000,000 3,500,000,000 3,500,000,000 5,000,000
Common stock, non-voting shares authorized       70,000,000     100,000
Common stock, par value         $ 0.01 $ 0.01  
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  
Common stock, shares, outstanding         334,461,630 334,461,630  
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        
Common stock, par value         $ 0.01    
Proceeds from issue of shares     $ 1,202.8        
Underwriting discounts and commissions     67.1        
Estimated offering expenses     $ 8.1        
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            
Secondary Public Offering              
Class of Stock [Line Items]              
Number of share issued   36,000,000          
Common stock, par value   $ 28          
Number of shares sold   0          
Secondary Public Offering | Carlyle              
Class of Stock [Line Items]              
Common stock shares outstanding percentage   54.10%          
Secondary Public Offering | GIC              
Class of Stock [Line Items]              
Common stock shares outstanding percentage   12.20%