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Share-Based Compensation - 2019 Stock-Based Incentive Compensation Plan (Details) - USD ($) | 12 Months Ended
--- | ---
Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Shareholders' Equity and Share-Based Payments |  |  |
Common stock, shares authorized (in shares) | 75,000,000 | 75,000,000 |
Options |  |  |
Outstanding at the beginning of the period (in shares) | 224,374 | 57,584 |
Outstanding at the end of the period (in shares) | 361,613 | 224,374 | 57,584
2019 Plan |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Number of shares of common stock available for awards | 750,000 |  |
Common stock, shares authorized (in shares) | 139,691 |  |
2019 Plan | Employee and Non Employee Stock Option |  |  |
Options |  |  |
Outstanding at the beginning of the period (in shares) | 224,374 | 57,584 |
Granted (in shares) | 161,613 | 224,374 | 0
Exercised (in shares) |  | (57,584) |
Cancelled (in shares) | (24,374) |  |
Outstanding at the end of the period (in shares) | 361,613 | 224,374 | 57,584
Vested and expected to vest (in shares) | 225,000 |  |
Weighted Average Exercise Price |  |  |
Outstanding at the beginning of the period (in dollars per share) | $ 8.19 | $ 7.1 |
Granted (in dollars per share) | 7.7 | 8.19 |
Exercised (in dollars per share) |  | 7.1 |
Cancelled (in dollars per share) | 8.21 |  |
Outstanding at the end of the period (in dollars per share) | 7.97 | $ 8.19 | $ 7.1
Vested and expected to vest (in dollars per share) | $ 8.18 |  |
Aggregate Intrinsic Value |  |  |
Outstanding at the beginning of the period (in dollars) |  | $ 88,104 |
Exercised (in dollars) |  | $ 28,792 |
Outstanding at the end of the period (in dollars) |  |  | $ 88,104

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