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Net Income (loss) per Share - Schedule of securities were not included in the computation of diluted shares outstanding (Detail)
9 Months Ended
Sep. 30, 2023
shares
PubCo Warrants - Public and Private  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 43,848,750
PubCo Class E Common Stock - Earnouts Units  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 1,075,761
BT OpCo Founder Convertible Preferred Units  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 2,900,000
BT OpCo Exchangeable Non-Controlling Interest  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 41,200,000
BT OpCo Earnouts Units  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 15,000,000
2023 Incentive Plan RSU awards  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 1,853,330
BitAccess Stock Options  
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]  
Number of securities 44,880