Horizontal: wherein the rook attacks down a rank.
I wish to know the fastest possible castling checkmates, for both queenside and kingside, that are a horizontal one
See my question about vertical castling here.
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Kingside castling, 8.5 moves (fastest; no way for a king to reach the last rank any faster than this.)
[FEN ""] 1. e4 d6 2. b4 Kd7 3. Nh3 Kc6 4. Bb5+ Kxb5 5. Nc3+ Kxb4 6. Ba3+ Kxa3 7. Qh5 Kb2 8. Qb5+ Kxa1 9. O-O#
Queenside castling: 8.5 moves (again, fastest.)
[FEN ""] 1. d4 e6 2. g4 Ke7 3. Na3 Kf6 4. Bg5+ Kxg5 5. Nf3+ Kxg4 6. Bh3+ Kxh3 7. Qd3 Kg2 8. Qg6+ Kxh1 9. O-O-O#
There you have it. The theoretical fastest is 8.0 moves if you try to let black deliver mate instead of white, but I couldn't find a way to set up the mating net or to avoid locking the king out. Feel free to try.