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3
Going to the dusty databanks in my skull, it turns ott, as I indeed recalled, albeit rather vaguely, that this indeed has already been addressed in Journey Entry #153 of Tim Krabbe's Chess Diary. Since you define the record as to how many plies before the actual mate, the given games there indeed match your findings of a 5.5 move game. Although, the entry ...
3
12 moves (24 plies), adapting Loyd's classic 19-ply help-stalemate:
[FEN ""]
1. d3 a5 2. Qd2 Ra6 3. Qxa5 h5 4. Qxc7 Rah6 5. Qxb7 f6 6. Qxb8 d6 7. h4 Bf5 8. Rh3 Kf7 9. Qxd6 Bh7 10. Qe6+ Kg6 11. f4 Qxd3 12. Kf2 Qg3+
and White must choose between 13 Kxg3 stalemate and 13 Rxg3 checkmate.
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