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Common Stock, Preferred Stock and Stockholders' (Deficit) Equity - Additional Information (Detail)
 3 Months Ended 9 Months Ended 12 Months Ended
Sep. 30, 2024
Series
$ / shares
shares
Sep. 30, 2024
USD ($)
Series
$ / shares
shares
Sep. 30, 2023
shares
Sep. 30, 2024
USD ($)
Series
$ / shares
shares
Jun. 30, 2024
Dec. 31, 2023
shares
Sep. 22, 2023
USD ($)
Jun. 30, 2023
shares
Schedule Of Stockholders Equity [Line Items]                
Shares, issued 2,223,250,000 2,223,250,000   2,223,250,000        
Share repurchase, amount | $   $ 158,000            
Share repurchase, average cost per share | $ / shares $ 2.26 $ 2.26   $ 2.26        
Share repurchase, shares 0 69,976 0          
Number of warrants outstanding 43,848,750 43,848,750   43,848,750        
Class of warrant or right exercise price | $ / shares $ 11.5 $ 11.5   $ 11.5        
Number of consecutive trading days for determining share price   20 days            
Number of trading days for determining the share price   10 days            
Class of warrants or rights expiration period   5 years            
BT Assets [Member]                
Schedule Of Stockholders Equity [Line Items]                
Equity ownership percentage         4.30%      
Public Warrants [Member]                
Schedule Of Stockholders Equity [Line Items]                
Number of warrants outstanding 31,625,000 31,625,000   31,625,000        
Private Warrants [Member]                
Schedule Of Stockholders Equity [Line Items]                
Number of warrants outstanding 12,223,750 12,223,750   12,223,750        
Maximum [Member]                
Schedule Of Stockholders Equity [Line Items]                
Authorized repurchase amount | $             $ 10,000,000  
Class A Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 800,000,000 800,000,000   800,000,000   800,000,000    
Common stock, vote per share   one vote            
Share repurchase, amount | $       $ 400,000        
Share repurchase, shares       190,620        
Class of warrant or right, number of securities called by each warrant or right 1 1   1        
Earn out provision share price | $ / shares $ 12 $ 12   $ 12        
Class A Common Stock [Member] | Share Price Equal Or Exceeds Eighteen Rupees Per Dollar [Member]                
Schedule Of Stockholders Equity [Line Items]                
Class of warrant or right per share price during the period | $ / shares 0.01 0.01   0.01        
Share price | $ / shares 18 $ 18   18        
Number of consecutive trading days for determining share price   20 days            
Number of trading days for determining the share price   30 days            
Right to redeem outstanding warrants once exercisable and prior to expiration | $ / shares $ 0.01 $ 0.01   $ 0.01        
Class B Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 20,000,000 20,000,000   20,000,000   20,000,000    
Common stock, vote per share   one vote            
Class M Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 300,000,000 300,000,000   300,000,000        
Common stock, vote per share   ten votes            
Class O Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 800,000,000 800,000,000   800,000,000        
Common stock, vote per share   one vote            
Class V Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 300,000,000 300,000,000   300,000,000        
Common stock, conversion basis   one-for-one            
Common stock percentage of voting rights 20.00% 20.00%   20.00%        
Class V Common Stock [Member] | BT Assets [Member]                
Schedule Of Stockholders Equity [Line Items]                
Forfeiture of shares 0 2,906,976            
Class E Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 2,250,000 2,250,000   2,250,000   2,250,000    
Number of common stock series | Series 3 3   3        
Earnout shares issuable 15,000,000 15,000,000   15,000,000        
Common stock, conversion basis   one-for-one            
Class E Common Stock [Member] | Sponsor [Member]                
Schedule Of Stockholders Equity [Line Items]                
Earnout shares issuable 1,075,061 1,075,061   1,075,061        
Class E-1 Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 750,000 750,000   750,000        
Class E-2 Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 750,000 750,000   750,000        
Class E-3 Common Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Common stock, shares authorized 750,000 750,000   750,000        
Series A Preferred Stock [Member]                
Schedule Of Stockholders Equity [Line Items]                
Preferred stock, shares issued 3,075,000 3,075,000   3,075,000   3,125,000   4,300,000
Preferred stock, shares outstanding 3,075,000 3,075,000   3,075,000   3,125,000    
Convertion of preferred shares 0 50,000