Shareholders' Equity and Share-Based Payments - Share-based compensation expense (Details) - USD ($)	3 Months Ended		6 Months Ended
	Mar. 31, 2026	Mar. 31, 2025	Mar. 31, 2026	Mar. 31, 2025
Share-Based Compensation
Share-based compensation expense	$ 496,294	$ 405,042	$ 1,412,218	$ 801,703
Cost of sales
Share-Based Compensation
Share-based compensation expense	18,638	18,261	56,180	40,260
Research and development
Share-Based Compensation
Share-based compensation expense	28,340	20,722	82,493	45,685
Selling, general and administrative
Share-Based Compensation
Share-based compensation expense	$ 449,316	$ 366,059	$ 1,273,545	$ 715,758