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Stock-Based Compensation (Details) - USD ($)
12 Months Ended
Dec. 22, 2023
Sep. 30, 2024
Sep. 30, 2023
Stock-Based Compensation [Abstract]      
Aggregate intrinsic value of stock options outstanding   $ 0  
Stock-based compensation expense   229,605 $ 370,878
Unrecognized share-based compensation   $ 5,603  
Weighted average remaining term   3 months  
Common stock shares (in Shares) 125,000