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Risks and Liquidity - Narrative (Details) - USD ($)
 1 Months Ended 3 Months Ended 9 Months Ended
Dec. 31, 2021
Oct. 31, 2021
Jun. 30, 2021
Apr. 30, 2021
Mar. 31, 2021
Sep. 30, 2021
Sep. 30, 2022
Unusual Risk or Uncertainty [Line Items]              
Accumulated deficit $ 29,254,440           $ 40,533,598
Cash and cash equivalents $ 49,635,197           $ 39,427,118
Conversion of preferred stock into common stock (in shares)   4,853,533          
Warrants prior to conversion (in shares)   480,415         5,860,000
Shares issued upon conversion of warrants (in shares)   9,816          
Proceeds from initial public offering   $ 24,400,000          
Series A Preferred Stock              
Unusual Risk or Uncertainty [Line Items]              
Temporary equity new shares issued     $ 1,948,309 $ 5,000,000 $ 3,034,526 $ 5,000,000  
Placement Agent Warrants              
Unusual Risk or Uncertainty [Line Items]              
Number of securities called by warrants (in shares)   250,000          
Warrants, term from date of issuance   5 years          
Warrant exercise price (in dollars per share)   $ 6.25          
December 2021 Private Placement Warrants              
Unusual Risk or Uncertainty [Line Items]              
Number of securities called by warrants (in shares) 5,000,000            
Warrants, term from date of issuance 5 years 6 months            
Warrant exercise price (in dollars per share) $ 6.25            
Issued in connection with 2021 private placement              
Unusual Risk or Uncertainty [Line Items]              
Number of securities called by warrants (in shares) 250,000            
Warrants, term from date of issuance 5 years 6 months            
Warrants prior to conversion (in shares)             5,250,000
Warrant exercise price (in dollars per share) $ 6.25           $ 6.25
IPO              
Unusual Risk or Uncertainty [Line Items]              
Number of shares issued in transaction   5,750,000          
Sale of stock, price per share (in dollars per share)   $ 5.00          
Private Placement              
Unusual Risk or Uncertainty [Line Items]              
Number of shares issued in transaction 5,000,000            
Sale of stock, price per share (in dollars per share) $ 6.25            
Stock issuance, consideration received $ 28,900,000