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