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Stock-Based Compensation (Details) - USD ($)
3 Months Ended 6 Months Ended
Jan. 01, 2024
Mar. 31, 2024
Mar. 31, 2023
Mar. 31, 2024
Mar. 31, 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   65,000 56,781 1,225,669 130,512      
Weighted-average grant date fair value (in Dollars per share)   $ 0.91 $ 0.88 $ 1.08 $ 0.75      
Total share based expenses (in Dollars)   $ 356,858 $ 237,628 $ 665,496 $ 537,809      
Total number of stock options outstanding   2,879,096   2,879,096     1,708,427  
Stock option vested   48,295 84,778 104,911 212,224      
Stock options, forfeited   0 0 55,000 0      
Options were exercised (in Dollars)        
Future issuance   183,130   183,130        
Unrecognized stock-based compensation (in Dollars)   $ 3,100,000   $ 3,100,000        
Weighted average period       2 years 8 months 12 days        
Restricted Stock Units (RSUs) [Member]                
Stock-Based Compensation [Line Items]                
Granted shares   1,006,725 61,728 1,006,725 61,728      
Total share based expenses (in Dollars)   $ 142,670 $ 95,625 $ 263,877 $ 214,062      
Weighted-average grant date fair value (in Dollars per share)   $ 1.03 $ 1.62 $ 1.03 $ 1.62      
Restricted stock units (in Dollars per share)   $ 32,535 $ 219,880 $ 70,214 $ 241,810      
Restricted stock units forfeited        
Stock Options [Member]                
Stock-Based Compensation [Line Items]                
Total share based expenses (in Dollars)   $ 214,188 $ 142,003          
Equity Option [Member]                
Stock-Based Compensation [Line Items]                
Total share based expenses (in Dollars)       $ 401,619 $ 323,747      
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