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