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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 |  |  |
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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 |  |

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