In the Pittman sale catalogue (Part One), David Akers recounted John McCloskey's assertion that there are eight different varieties of the 1835 Classic Head Half Eagle. Only three Proofs are known of this date, all from the same pair of dies. Breen illustrates an unattributed Proof 1835 Half Eagle (Breen 6506) which is most likely the Smithsonian's example.
Nearly straight truncation line, Small Date
Curved truncation line, Small Date
Curved truncation line, Large Date (illustrated above)
Sources and/or recommended reading:
"Walter Breen's Complete Encyclopedia of U.S. and Colonial Coins" by Walter Breen