Breen (1989) listed Proof examples of four different 1831 Half Dime varieties: LM-4, LM-5, LM-6, and LM-7.
According to Logan and McCloskey (1998), "The paucity of new working dies in 1831 resulted in some interesting die states that have been erroneously interpreted by many twentieth century numismatists as proofs." The Mint was obviously doing its best to extend the life of Reverse L, and in the process, lapped and polished this die extensively. Although Breen never reported any proof example of LM-1, recent auction descriptions have declared many of these coins proofs, hardly indicative of the quality that the Mint was capable of producing when it tried." With this is mind, they list "proof knowns" for LM-1.2, LM-3, LM-4, and LM-7.
Sources and/or recommended reading:
"Walter Breen's Encyclopedia of United States and Colonial Proof Coins 1722-1989, New Revised and Corrected Edition" by Walter Breen (1989).
"Federal Half Dimes 1792-1837" by Russell J. Logan and John W. McCloskey (1998)