Stock-Based Compensation - Option Assumptions (Details) - Employee Stock Option - USD ($)	3 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Share-based Compensation
Risk-free interest rate	3.50%	4.60%
Expected term (years)	5 years 6 months	5 years 6 months
Expected volatility	134.00%	130.60%
Expected dividend yield	0.00%	0.00%
Unrecognized compensation expense	$ 6,496,794
Unrecognized compensation exercise period	9 months 18 days