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Common Stock, Preferred Stock and Stockholders' (Deficit) Equity - Additional Information (Detail)
3 Months Ended 6 Months Ended 9 Months Ended 12 Months Ended
Oct. 06, 2025
$ / shares
shares
Jul. 01, 2025
USD ($)
$ / shares
May 30, 2025
shares
Nov. 20, 2024
USD ($)
$ / shares
Sep. 30, 2025
USD ($)
Series
$ / shares
shares
Mar. 31, 2024
USD ($)
shares
Jun. 30, 2024
USD ($)
$ / shares
shares
Sep. 30, 2025
USD ($)
Series
$ / shares
shares
Sep. 30, 2024
USD ($)
Jun. 30, 2024
USD ($)
$ / shares
shares
Dec. 31, 2024
USD ($)
$ / shares
shares
Mar. 31, 2025
shares
Sep. 22, 2023
USD ($)
Jun. 30, 2023
shares
Schedule Of Stockholders Equity [Line Items]                            
Shares, issued         2,272,250,000     2,272,250,000            
Distribution paid | $               $ 10,117,000 $ 22,748,000          
Share repurchase, amount | $           $ 158,000 $ 200,000              
Authorized repurchase amount | $                         $ 10,000,000  
Share repurchase, shares           69,976 69,976              
Share repurchase, average cost per share | $ / shares             $ 2.26     $ 2.26        
Number of warrants outstanding         43,848,750     43,848,750            
Class of warrant or right exercise price | $ / shares         $ 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            
Common stock for net proceeds | $               $ 20,847,000 $ 0          
BT Hold Co [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Distribution paid | $                     $ 29,000,000      
Conversion of stock, description               During the three months ended March 31, 2025, the holders of the Series A Preferred Stock exercised their option to convert the Series A Preferred Stock for Class A Common Stock on a 1:1 basis.            
New ATM Equity Offering Program [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Sale of shares amount | $   $ 50,000,000                        
Original ATM Equity Offering [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, par or stated value per share | $ / shares   $ 0.0001   $ 0.0001                    
Sale of shares amount | $   $ 25,000,000                        
BT Assets [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Equity Method Investment, Ownership Percentage                 4.30%          
Public Warrants [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Number of warrants outstanding         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            
Maximum [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Sale of shares amount | $   $ 100,000,000                        
Class A Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, vote per share               one vote            
Common stock, shares authorized         800,000,000     800,000,000     800,000,000      
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            
Earn out provision share price | $ / shares         $ 12     $ 12            
Common stock, shares, issued         27,938,182     27,938,182     19,263,164      
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001     $ 0.0001      
Class A Common Stock [Member] | Subsequent Event [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Share repurchase, average cost per share | $ / shares $ 3.5                          
Common stock, par or stated value per share | $ / shares $ 0.0001                          
Stock issued during the period shares new issues 4,285,716                          
Class A Common Stock [Member] | At-the Market Equity Offering [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock aggregate offering amount maximum | $       $ 13,100,000                    
Market capitalization | $       75,000,000                    
Market capitalization exceeds | $       75,000,000                    
Aggregate offering amount increases | $       $ 25,000,000                    
Stock issued during the period shares new issues         1,796,633     4,716,963            
Common stock for net proceeds | $         $ 8,900,000     $ 20,900,000            
Equity offering program remained available for issuance | $               $ 29,100,000            
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            
Share price | $ / shares         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            
Class B Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, vote per share               one vote            
Common stock, shares authorized         20,000,000     20,000,000            
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001            
Class M Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, vote per share               ten votes            
Common stock, shares authorized         300,000,000     300,000,000            
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001            
Class M Common Stock [Member] | Up-C Restructuring [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Conversion of common stock shares     41,193,024                      
Class O Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, vote per share               one vote            
Common stock, shares authorized         800,000,000     800,000,000            
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001            
Class V Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares authorized         300,000,000     300,000,000            
Common stock percentage of voting rights         20.00%     20.00%            
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001            
Class V Common Stock [Member] | BT Assets [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Forfeiture of shares                     2,906,976      
Class V Common Stock [Member] | Up-C Restructuring [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares, issued     41,193,024                      
Class E Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares authorized         2,250,000     2,250,000     2,250,000      
Number of common stock series | Series         3     3            
Earnout shares issuable         15,000,000     15,000,000            
Common stock, shares, issued         0     0     1,075,761      
Common stock, par or stated value per share | $ / shares         $ 0.0001     $ 0.0001     $ 0.0001      
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 Common Stock [Member] | Up-C Restructuring [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Earnout shares issuable     15,000,000                      
Contingent equity rights     15,000,000                      
Class E-1 Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares authorized         750,000     750,000            
Class E-2 Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares authorized         750,000     750,000            
Class E-3 Common Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Common stock, shares authorized         750,000     750,000            
Series A Preferred Stock [Member]                            
Schedule Of Stockholders Equity [Line Items]                            
Preferred stock, shares issued         0     0     1,733,884     4,300,000
Preferred stock, shares outstanding         0     0     1,733,884      
Convertion of preferred shares           50,000           1,733,884