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Stock-Based Compensation (Details) - USD ($)		3 Months Ended		9 Months Ended
Stock-Based Compensation (Details) - USD ($)	Jan. 01, 2024	Jun. 30, 2024	Jun. 30, 2023	Jun. 30, 2024	Jun. 30, 2023	Nov. 09, 2023	Sep. 30, 2023	Oct. 04, 2021
Stock-Based Compensation [Line Items]
Shares outstanding percentage				13.00%
Option plan shares	1,051,556
Granted shares		0	339,000	1,225,669	469,512
Weighted-average grant date fair value (in Dollars per share)			$ 0.92	$ 1.08	$ 0.88
Total share based expenses (in Dollars)		$ 338,609	$ 296,402	$ 1,004,105	$ 834,211
Total number of stock options outstanding		2,814,096		2,814,096			1,708,427
Stock option vested		127,583	69,947	232,494	282,172
Stock options, forfeited		65,000	521	120,000	521
Options were exercised (in Dollars)
Future issuance		289,215		289,215
Unrecognized stock-based compensation (in Dollars)		$ 2,713,998		$ 2,713,998
Weighted average period				2 years 6 months
Stock Options [Member]
Stock-Based Compensation [Line Items]
Total share based expenses (in Dollars)		202,338	158,528	$ 603,957	482,276
Restricted Stock Units (RSUs) [Member]
Stock-Based Compensation [Line Items]
Total share based expenses (in Dollars)		$ 136,271	$ 137,874	$ 400,148	$ 351,935
Granted shares		0	249,000	1,006,725	310,728
Weighted-average grant date fair value (in Dollars per share)			$ 1.59	$ 1.03	$ 1.6
Restricted stock units vest		162,309	52,299	232,523	294,109
Restricted stock units forfeited
Vesting Period [Member] \| Restricted Stock Units (RSUs) [Member]
Stock-Based Compensation [Line Items]
Other vesting, percentage					50.00%
Minimum [Member] \| Restricted Stock Units (RSUs) [Member]
Stock-Based Compensation [Line Items]
Vest over period					1 year
Maximum [Member] \| Restricted Stock Units (RSUs) [Member]
Stock-Based Compensation [Line Items]
Vest over period					3 years
NeuroOne Medical Technologies Corporation [Member]
Stock-Based Compensation [Line Items]
Future issuance shares								420,350
Inducement Plan [Member] \| Minimum [Member]
Stock-Based Compensation [Line Items]
Equity incentive awards under inducement plan						150,000
Inducement Plan [Member] \| Maximum [Member]
Stock-Based Compensation [Line Items]
Equity incentive awards under inducement plan						570,350