v3.26.1
Stockholder's Equity (Details) - USD ($)
 3 Months Ended 6 Months Ended
Mar. 24, 2026
Dec. 10, 2025
Dec. 08, 2025
Sep. 19, 2025
Sep. 10, 2025
Jul. 17, 2025
Mar. 31, 2026
Mar. 31, 2025
Mar. 31, 2026
Mar. 31, 2025
Oct. 27, 2025
Sep. 30, 2025
Jul. 16, 2025
Apr. 07, 2025
Aug. 05, 2024
Aug. 02, 2024
Apr. 29, 2023
Stockholder’s Equity [Line Items]                                  
Common stock authorized             400,000,000   400,000,000     400,000,000     110,000,000    
Common stock par value (in Dollars per share)             $ 0.0001   $ 0.0001     $ 0.0001          
Preferred stock authorized             10,000,000   10,000,000     10,000,000          
Preferred stock par value (in Dollars per share)             $ 0.0001   $ 0.0001     $ 0.0001          
Warrants purchase   816,738     5,142,858               6,818,182        
Exercise price per share (in Dollars per share)   $ 1.09     $ 1.09               $ 1.09        
Net proceeds (in Dollars)           $ 7,546,988                      
Expenses of placement agent fee (in Dollars)           $ 125,000                      
Warrant expire date   Jan. 20, 2031                              
Proceeds from exercise of pre-funded warrants (in Shares)             8,183,358                    
Proceeds from exercise of pre-funded warrants (in Dollars)             $ 818                    
Common stock reserved             38,653,029   38,653,029                
Aggregate shares of common stock             83,653,029   83,653,029                
Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Term of exercisable warrants           5 years                      
Exercise price per share (in Dollars per share)           $ 1.32                      
Warrant commencement date           Jan. 17, 2026                      
Common stock reserved             38,653,029   38,653,029                
Weighted average period                 3 years 11 months 19 days                
Warrants outstanding (in Dollars)             $ 4,367,815   $ 4,367,815                
Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase           272,727                      
Exercise price per share (in Dollars per share)           $ 1.65                      
Fair value of the warrants (in Dollars)           $ 905,000                      
Warrant expire date           Jul. 17, 2030                      
Percentage of placement agent cash fee           7.00%                      
December 2025 Offering Investors                                  
Stockholder’s Equity [Line Items]                                  
Exercise price per share (in Dollars per share)             $ 0.0001   $ 0.0001                
Common stock reserved             7,046,000   7,046,000                
2024 Plan [Member]                                  
Stockholder’s Equity [Line Items]                                  
Aggregate shares of common stock                     30,000,000            
Additional shares of common stock                     15,000,000            
Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Common stock authorized                             100,000,000    
Common stock par value (in Dollars per share)                             $ 0.0001    
Gross proceeds offering (in Dollars)           $ 9,000,000                      
Percentage of placement agent fee           7.00%                      
Proceeds from exercise of pre-funded warrants (in Shares)             8,183,358                    
Proceeds from exercise of pre-funded warrants (in Dollars)             $ 818                    
Common Stock [Member] | Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase           477,273                      
Exercise price per share (in Dollars per share)           $ 1.65                      
Warrant commencement date           Aug. 17, 2025                      
Warrant expire date           Jul. 17, 2030                      
Preferred Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Preferred stock authorized                             10,000,000    
Preferred stock par value (in Dollars per share)                             $ 0.0001    
Proceeds from exercise of pre-funded warrants (in Dollars)                                
Restricted Stock Award [Member]                                  
Stockholder’s Equity [Line Items]                                  
Stock-based compensation expense (in Dollars)             1,668,267   $ 3,372,282                
Restricted stock awards 350,000                                
Restricted stock awards date       Sep. 19, 2028                          
Unrecognized total compensation cost related to unvested restricted stock awards (in Dollars)             16,926,977   $ 16,926,977                
Weighted average period                 2 years 5 months 23 days                
Restricted Stock Award [Member] | Board of Directors [Member]                                  
Stockholder’s Equity [Line Items]                                  
Restricted stock awards       11,600,000                          
Restricted Stock Award [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Common stock on the date of grant (in Dollars)       $ 20,300,000         $ 203,000                
Common stock on the date of grant per share (in Dollars per share)       $ 1.75         $ 0.58                
Investor [Member] | Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Fair value of the warrants (in Dollars)     $ 5,301,000     $ 8,197,000                      
September Two Thousand Twenty Five Offering [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   5,142,858                              
Net proceeds (in Dollars)         $ 7,619,854                        
Percentage of placement agent fee         7.00%                        
Expenses of placement agent fee (in Dollars)         $ 125,000                        
Warrant commencement date         Mar. 10, 2026                        
Warrant expire date   Jan. 20, 2031     Mar. 10, 2031                        
Common stock per share (in Dollars per share)         $ 1.75                        
Gross proceeds from offering (in Dollars)         $ 9,000,000                        
September Two Thousand Twenty Five Offering [Member] | Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Exercise price per share (in Dollars per share)   $ 1.09     $ 1.84                        
Fair value of the warrants (in Dollars)     $ 4,179,000   $ 6,995,000                        
Warrant commencement date         Mar. 10, 2026                        
Warrant expire date         Mar. 10, 2031                        
September Two Thousand Twenty Five Offering [Member] | Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase         205,714                        
Exercise price per share (in Dollars per share)         $ 1.92                        
Fair value of the warrants (in Dollars)         $ 717,000                        
Warrant commencement date         Mar. 10, 2026                        
Warrant expire date         Mar. 10, 2031                        
Percentage of placement agent cash fee         7.00%                        
September Two Thousand Twenty Five Offering [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Shares of common stock         5,142,858                        
Warrants purchase         5,142,858                        
September Two Thousand Twenty Five Offering [Member] | Common Stock [Member] | Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase         360,000                        
Exercise price per share (in Dollars per share)         $ 2.1875                        
December 2025 Offering [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   16,513,762                              
Exercise price per share (in Dollars per share)   $ 1.09                              
Net proceeds (in Dollars)   $ 15,062,724                              
Percentage of placement agent fee   7.00%                              
Expenses of placement agent fee (in Dollars)   $ 135,000                              
Gross proceeds from offering (in Dollars)   $ 18,000,000                              
December 2025 Offering [Member] | Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Term of exercisable warrants   5 years                              
Warrant expire date   Dec. 08, 2030                              
December 2025 Offering [Member] | Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   1,155,963                              
Fair value of the warrants (in Dollars)   $ 1,401,000                              
Warrant expire date   Dec. 08, 2030                              
Percentage of placement agent cash fee   7.00%                              
December 2025 Offering [Member] | Pre-Funded Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Shares of common stock   15,229,358                              
Warrants purchase   15,229,358                              
Exercise price per share (in Dollars per share)   $ 0.0001                              
Pre-funded warrants exercisable   15,229,358                              
December 2025 Offering [Member] | Investors Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   16,513,762                              
Fair value of the warrants (in Dollars)   $ 13,196,000                              
December 2025 Offering [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Shares of common stock   1,284,404                              
Warrants purchase   1,284,404                              
Exercise price per share (in Dollars per share)   $ 1.199                              
December 2025 Offering [Member] | Common Stock [Member] | Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Exercise price per share (in Dollars per share)   $ 1.09                              
December 2025 Offering [Member] | Common Stock [Member] | Placement Agent Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   660,550                              
Exercise price per share (in Dollars per share)   $ 1.3625                              
December 2025 Offering [Member] | Common Stock [Member] | Pre-Funded Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Exercise price per share (in Dollars per share)   $ 1.0899                              
IPO [Member] | Warrants [Member]                                  
Stockholder’s Equity [Line Items]                                  
Warrants purchase   6,818,182                              
Exercise price per share (in Dollars per share)   $ 1.09                              
IPO [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Shares of common stock           6,818,182                      
Warrants purchase           6,818,182                      
Common stock price per share (in Dollars per share)           $ 1.32                      
Stock Plans [Member]                                  
Stockholder’s Equity [Line Items]                                  
Aggregate shares of common stock                               15,000,000 15,000,000
Contractual term                 10 years                
Stock-based compensation expense (in Dollars)             1,858,443 $ 2,088,572 $ 4,110,478 $ 3,897,050              
Unrecognized total compensation cost (in Dollars)             $ 3,704,204   $ 3,704,204                
Unrecognized total compensation cost                 1 year 7 days                
Minimum [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Common stock authorized                           100,000,000      
Maximum [Member] | Common Stock [Member]                                  
Stockholder’s Equity [Line Items]                                  
Common stock authorized                           400,000,000