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Share-Based Compensation - Fair Value assumptions for stock option plan (Details) - USD ($) | 12 Months Ended
--- | ---
Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Share-Based Compensation |  |  |
Share-based compensation expense | $ 1,003,292 | $ 1,336,000 | $ 345,000
2019 Plan | Employee and Non Employee Stock Option |  |  |
Share-Based Compensation |  |  |
Granted (in shares) | 161,613 | 224,374 | 0
Share-based compensation expense | $ 301,000 | $ 756,000 | $ 167,000
Unrecognized compensation cost, related to non-vested stock options | $ 495,797 |  |
2019 Plan | Employee and Non Employee Stock Option | Minimum |  |  |
Share-Based Compensation |  |  |
Vesting period | 3 years |  |
2019 Plan | Employee and Non Employee Stock Option | Maximum |  |  |
Share-Based Compensation |  |  |
Expiration term | 10 years |  |
Vesting period | 5 years |  |

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- Definition The period of time, from the grant date until the time at which the share-based option award expires. + References No definition available. + Details
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- Definition Amount of expense for award under share-based payment arrangement. Excludes amount capitalized. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 14.F) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479830/718-10-S99-1 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition. + References Reference 1: http://www.xbrl.org/2003/role/exampleRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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