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Recapitalization - Additional Information (Details) - USD ($)
$ / shares in Units, $ in Millions
9 Months Ended
Feb. 14, 2025
Sep. 30, 2025
Dec. 31, 2024
Sep. 30, 2024
Dec. 31, 2023
Share Repurchase Program [Line Items]          
Sale of common stock   1,150,000      
Common stock, shares outstanding   48,018,545 5,836,882 5,800,000  
Common stock, par value $ 0.0001 $ 0.0001 $ 0.0001    
Transaction costs incurred $ 14.0        
Common Stock [Member]          
Share Repurchase Program [Line Items]          
Common stock, shares outstanding   48,720,405 5,836,882 5,836,882 7,072,300
FTAC Emerald [Member]          
Share Repurchase Program [Line Items]          
Common stock, shares outstanding   14,237,038      
Net cash proceeds $ 0.8        
FTAC Emerald [Member] | Class A [Member]          
Share Repurchase Program [Line Items]          
Common stock, shares outstanding 10,932,855 10,932,855      
Common stock, par value $ 0.0001        
Common stock redeemed $ 3.3        
FTAC Emerald [Member] | Common Stock [Member]          
Share Repurchase Program [Line Items]          
Number of common shares issued and outstanding equity interests $ 372.0        
Sale of common stock 34,100,000        
FTAC Emerald [Member] | Common Stock [Member] | SAFEs [Member]          
Share Repurchase Program [Line Items]          
Sale of common stock 34,100,000