Ron Guth: Breen (1989) listed Proof examples of LM-1 only.
Logan and McCloskey (1998) were unable to verify any Proof examples of LM-1, or any other 1837 Half Dime varieties.
Thus, the existence of any Proof 1837 Half Dime is in doubt.
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)
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