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Share-Based Compensation - Restricted stock units related to the plan 2019 (Details) - USD ($) | 12 Months Ended
--- | ---
Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Shareholders' Equity and Share-Based Payments |  |  |
Share-based compensation expense | $ 1,003,292 | $ 1,336,000 | $ 345,000
Restricted Stock Units |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Number of securities called by each award vested | 1 |  |
Restricted stock units outstanding (in shares) | 242,080 | 101,968 | 32,897
Restricted Stock Units | Chief Executive Officer |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Vesting period | 3 years |  |
Restricted Stock Units | Chief Financial Officer |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Vesting period | 4 years |  |
Forfeiture period | 11,503 |  |
Restricted Stock Units | 2019 Plan |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Restricted stock units outstanding (in shares) | 242,080 | 101,968 | 32,897
Share-based compensation expense | $ 702,000 | $ 694,000 | $ 173,000
Unrecognized compensation expense | $ 1,384,896 |  |

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