Stock-Based Compensation - Option Assumptions (Details) - USD ($)	9 Months Ended
	Jun. 30, 2024	Jun. 30, 2023
Employee Stock Option [Member]
Share-based Compensation
Risk-free interest rate	4.30%	3.70%
Expected term (years)	6 years	5 years 10 months 24 days
Expected volatility	131.30%	111.70%
Expected dividend yield	0.00%	0.00%
Unrecognized compensation expense	$ 8,818,798
Unrecognized compensation exercise period	1 year 6 months
Performance-based stock options
Share-based Compensation
Risk-free interest rate	4.30%	3.80%
Expected term (years)	10 years	10 years
Expected volatility	125.60%	91.30%
Expected dividend yield	0.00%	0.00%