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Non-controlling interests - Additional Information (Detail) - USD ($)
$ in Millions
 9 Months Ended
Sep. 30, 2024
Dec. 31, 2023
Class V Common Stock [Member]    
Noncontrolling Interest [Line Items]    
Common stock, shares outstanding 41,193,024  
Majority Stockholder of Lux Vending LLC, BT Assets, Inc    
Noncontrolling Interest [Line Items]    
Number of common units issued of limited liability company 41,193,024  
Number of preferred units issued of limited liability company 2,900,000  
Shares exchanged as part of transaction 2,906,976  
Majority Stockholder of Lux Vending LLC, BT Assets, Inc | Class V Common Stock [Member]    
Noncontrolling Interest [Line Items]    
Common stock, shares outstanding 41,193,024  
Bit Access [Member] | Non-controlling Interest [Member]    
Noncontrolling Interest [Line Items]    
Non-controlling interest ownership percentage 17.86% 17.86%
BT Hold Co [Member]    
Noncontrolling Interest [Line Items]    
Non-controlling interest ownership percentage 67.82% 72.50%
Number of common units issued of limited liability company 41,193,024 44,100,000
BT Hold Co [Member] | Majority Stockholder of Lux Vending LLC, BT Assets, Inc    
Noncontrolling Interest [Line Items]    
Preferred unit liquidation preference per share 10.00%  
Preferred unit liquidation preference value $ 29.0  
BT Hold Co [Member] | Maximum [Member]    
Noncontrolling Interest [Line Items]    
Allocation of net income $ 29.0  
BT Hold Co [Member] | Non-controlling Interest [Member]    
Noncontrolling Interest [Line Items]    
Non-controlling interest ownership percentage 67.80% 72.60%
Redeemable non-controlling interest, equity, fair value $ 6.7 $ 25.2