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Stock-Based Compensation (Details) - USD ($)
3 Months Ended
Jan. 01, 2024
Dec. 31, 2023
Dec. 31, 2022
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   1,160,669 73,731      
Weighted-average grant date fair value (in Dollars per share)   $ 1.08 $ 0.66      
Total share based expenses (in Dollars)   $ 308,638 $ 300,181      
Total number of stock options outstanding   2,814,096     1,708,427  
Stock option vested   56,616 127,446      
Stock options, forfeited   55,000 0      
Future issuance shares   182,314        
Unrecognized share based compensation (in Dollars)   $ 2,372,540        
Weighted average period   2 years 6 months        
Minimum [Member] | Inducement Plan [Member]            
Stock-Based Compensation [Line Items]            
Increase to inducement plan reserve for future stock issuances       150,000    
Maximum [Member] | Inducement Plan [Member]            
Stock-Based Compensation [Line Items]            
Increase to inducement plan reserve for future stock issuances       570,350    
NeuroOne Medical Technologies Corporation [Member]            
Stock-Based Compensation [Line Items]            
Future issuance shares           420,350
Stock Options [Member]            
Stock-Based Compensation [Line Items]            
Total share based expenses (in Dollars)   $ 187,431 $ 181,744      
Restricted Stock Units (RSUs) [Member]            
Stock-Based Compensation [Line Items]            
Total share based expenses (in Dollars)   $ 121,207 $ 118,437      
RSU vested   37,679 21,930