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Other Long-Term Liabilities (Details) - USD ($)
9 Months Ended 12 Months Ended
Apr. 16, 2024
Sep. 30, 2024
Sep. 30, 2023
Dec. 31, 2023
Dec. 31, 2022
Jun. 30, 2024
Bonus Rights [Member]            
Other Long-Term Liabilities [Line Items]            
Maximum number of shares granted (in Shares)         370,448  
Vested rights per share (in Dollars per share)         $ 40  
Earned shares (in Shares)   95,071 95,071 95,071 71  
Recognized a bonus right liability   $ 74,250   $ 84,125    
General and administrative expenses   4,381 $ 4,382 75,830 $ 8,295  
Research and development expenses   5,494 $ 1,236      
Unrecognized compensation expense   $ 462,269   $ 14,660 $ 125,725  
Bonus right awards are expected to vest (in Shares)   106,396   97,483 97,785  
Bonus Rights [Member] | Previously Reported [Member]            
Other Long-Term Liabilities [Line Items]            
Recognized a bonus right liability       $ 84,125   $ 8,295
Bonus Rights [Member] | Maximum [Member]            
Other Long-Term Liabilities [Line Items]            
Grant price (in Dollars per share) $ 40          
Bonus Rights [Member] | Minimum [Member]            
Other Long-Term Liabilities [Line Items]            
Grant price (in Dollars per share) $ 30          
Unvested Bonus Rights [Member]            
Other Long-Term Liabilities [Line Items]            
Recognized a bonus right liability       $ 56,988