What are the fastest vertical checkmates for both castlings? Vertical: wherein the rook attacks down a file.

I wish to know the fastest possible castling checkmates, for both queenside and kingside, that are a vertical one.

See my question about horizontal castling here.
Mate in 6.0 for kingside.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1 "]
1. e4 e6 2. Bc4 Bd6 3. Ke2 Qg5 4. Kf3 Nh6 5. Bxe6 fxe6 6. Qe2 O-O#


And 5.5 for queenside, even faster.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1 "]
1. d4 Nc6 2. Nc3 Nxd4 3. Qxd4 e5 4. Qc4 Ke7 5. Bg5+ Kd6 6. O-O-O#


This should be fastest.