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Shareholders' Equity and Share-Based Payments (Details) - USD ($) | 3 Months Ended |
--- | --- | ---
Dec. 31, 2023 | Dec. 31, 2022 | Sep. 30, 2023
Shareholders' Equity and Share-Based Payments |  |  |
Common stock, shares authorized (in shares) | 75,000,000 |  | 75,000,000
Preferred stock, shares authorized (in shares) | 10,000,000 |  | 10,000,000
2019 Plan |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Common stock, shares authorized (in shares) | 139,691 |  |
Share-based compensation expense | $ 205,716 | $ 283,195 |
Unrecognized compensation cost, related to non-vested stock options | $ 554,185 |  |
2019 Plan | Maximum |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Number of shares of common stock reserved for awards | 750,000 |  |
2019 Plan | Employee |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Share-based compensation expense | $ 155,581 | 233,125 |
2019 Plan | Non Employee Director |  |  |
Shareholders' Equity and Share-Based Payments |  |  |
Share-based compensation expense | $ 50,135 | $ 50,070 |

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