The 1831 Half Dollar is extremely rare in Proof condition. In recent years, four demonstrably different examples have been confirmed. Older auction citations refer to additional pieces but those coins have either not been examined by experts in recent years or they may be one of the examples known today. Unfortunbately, there is no way to confirm the connection. Heritage sold the finest known example (a PCGS PR65) at auction in April 2013 for $79,312.50.
Of the four known 1831 Half Dollar Proofs, three are of the Overton-103 variety, and one is of the Overton-108 variety.