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Convertible Preferred Stock, Redeemable Common Stock and Common Stock - Narrative (Details) - USD ($)
 1 Months Ended 3 Months Ended 9 Months Ended 12 Months Ended
Sep. 30, 2021
Dec. 31, 2021
Oct. 31, 2021
Feb. 28, 2021
Jun. 30, 2021
Apr. 30, 2021
Mar. 31, 2021
Sep. 30, 2022
Sep. 30, 2021
Dec. 31, 2021
Mar. 31, 2022
Class of Warrant or Right [Line Items]                      
Warrants prior to conversion (in shares)     480,415         5,860,000      
Converted amount               $ 0 $ 5,866,290    
Warrants reclassified into additional paid-in-capital       $ 100,000              
Conversion of convertible notes to preferred stock (in shares)     4,853,533                
Proceeds from initial public offering     $ 24,400,000                
Fair value of warrants for services provided               $ 0 371,895    
Common Stock                      
Class of Warrant or Right [Line Items]                      
Conversion of preferred shares and redeemable common shares 4,853,533                    
IPO                      
Class of Warrant or Right [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                      
Class of Warrant or Right [Line Items]                      
Number of shares issued in transaction   5,000,000                  
Sale of stock, price per share (in dollars per share)   $ 6.25               $ 6.25  
Stock issuance, consideration received   $ 28,900,000                  
Issued in connection with 2021 IPO                      
Class of Warrant or Right [Line Items]                      
Warrants prior to conversion (in shares)     250,000     24,134   250,000      
Warrant exercise price (in dollars per share)     $ 6.25     $ 7.168   $ 6.25      
Warrants, term from date of issuance     5 years                
Issued to Series A Stockholders                      
Class of Warrant or Right [Line Items]                      
Warrants prior to conversion (in shares)           184,597          
Warrant exercise price (in dollars per share)           $ 7.168          
Issued in Connection with IPO | Common Stock                      
Class of Warrant or Right [Line Items]                      
Conversion of convertible notes to preferred stock (in shares) 9,816                    
December 2021 Private Placement Warrants                      
Class of Warrant or Right [Line Items]                      
Warrant exercise price (in dollars per share)   $ 6.25               $ 6.25  
Warrants, term from date of issuance   5 years 6 months               5 years 6 months  
Number of securities called by warrants (in shares)   5,000,000               5,000,000  
Issued in connection with 2021 private placement                      
Class of Warrant or Right [Line Items]                      
Warrants prior to conversion (in shares)               5,250,000      
Warrant exercise price (in dollars per share)   $ 6.25           $ 6.25   $ 6.25  
Warrants, term from date of issuance   5 years 6 months               5 years 6 months  
Number of securities called by warrants (in shares)   250,000               250,000  
Issued in 2022 for consulting services                      
Class of Warrant or Right [Line Items]                      
Warrants prior to conversion (in shares)               360,000     360,000
Warrant exercise price (in dollars per share)               $ 10.00     $ 10.00
Warrants, term from date of issuance                     5 years 9 months 3 days
Fair value of warrants for services provided                   $ 300,000  
Senior Convertible Notes, April 2020 | Convertible Notes Payable                      
Class of Warrant or Right [Line Items]                      
Converted amount       $ 6,100,000              
Series A Preferred Stock                      
Class of Warrant or Right [Line Items]                      
Temporary equity new shares issued (in shares)         285,351 738,445 453,094        
Temporary equity, price per share (in dollars per share)           $ 7.168          
Temporary equity new shares issued         $ 1,948,309 $ 5,000,000 $ 3,034,526   $ 5,000,000    
Series A Preferred Stock | Senior Convertible Notes, April 2020 | Convertible Notes Payable                      
Class of Warrant or Right [Line Items]                      
Shares issued as a result of converted debt (in shares)       844,824              
Debt conversion, price per share (in dollars per share)       $ 7.168