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Stock-Based Compensation - Assumptions Used to Value Stock Options (Details) - $ / shares
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Share-Based Payment Arrangement [Abstract]      
Expected dividend yield 0.00% 0.00% 0.00%
Risk-free interest rate, minimum 3.69%   0.40%
Risk-free interest rate, maximum 4.57%   1.10%
Volatility 86.40%    
Volatility, minimum     86.20%
Volatility, maximum     90.40%
Expected term (in years) 6 years 3 months   6 years 3 months
Weighted-average grant date fair value per share $ 25.61   $ 48.64