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'The Cavalier is a sort of multipath Gryphon, which cannot stop on any
adjacent square. Benjamin C. Good wrote (March 13, 2002) that this piece
cannot, in general, force mate - because it does not attack adjacent
squares.'

Well, pieces that do not attack at least two orthogonally adjacent squares
obviously can not checkmate. But the Cavalier obiously attacks lots of
adjacent squares. I think the percieed problem was that the rays covered b
the Cavalier are not 'air tight', but have a hole in them, allowing the
bre King to escape its confines by approaching the Cavalier. A Cavalier,
unlike a Rook, can not change to another position alog the ray it covers.

The mate is very easy, though, (even on infinite boards) as a Cavalier can
also do things a Rook cannot do. You don't even need a corner, just an
edge (say 1st rank), and it works on an infinite board.It works like
this:

1) Cut off the bare King from moving away from the edge, (a rank, say),
and walk your own King to be further from the edge than he is.

2) Cut off the bare King moving laterally away from the file your own King
is in, and step towards his file, staying further from the edge than he
is.

3) When the Kings are nearly in the same file, position the Cavalier in
the file of the bare King, so that he gets trapped in the 'corridor'
between the Cavalier's attack lines.

4) Use your King to push the bare King towards the edge, walking on the
same file, until he reaches 1st rank (on f1, say).

5) Lift the stalemate danger by moving your Cavalier to a file far away,
so you can safely take opposition on 3rd rank.

6) We now have to get the bare King into opposition twice, once for
driving him back to 1st rank with check along the rank, second time for
checkmating. In both cases we shephard him into opposition by first taking
opposition ourself, and when he steps sideways, cut off the file two files
away from our King. He then either has to step back into opposition, or
step back immediately.

The main problem is keeping enough distance, as the Cavalier has thes
'holes' in its attack set nearby. So in general, when advancing towards
the edge, for sideway checking, we move one file away from the bare King.
On a small board this might not be possible, and we have to manouevre a
bit. This takes some extra moves, but the principle remains the same.
e.g.:

w: Kd4, Cd8 b: Kd2

1. ... Kd1, 2. Cg7 (out of the way), Kc2 3. Ca8 (cut off b-file), Kd2

Now we would have liked to check from the side, but our Cavalier is on  on
the a-file, and the b-file is too close to cover c2. So we nudge him to the
other side:

4. Cb6 (cut off c-file), Ke2 5. Cg7 (cut off f-file), Kd2 6. Ch3+ (got
him!), Ke1 7. Ke3 (opposition), Kf1

Now we would have liked to cut off the g-file, but our Cavalier is already
on the h-file, and too close to cover f2. And even if he was, we are in
zugzwang. So again some delay displacing the position sideways to gain
room, and then nudge him to the long side:

8. Kf3 (opposition), Ke1 (only move, g1 was attacked) 9. Cc5 (cut off
d-file) , Kf1 10. Cb2#.

Easy as pie...