What a beautiful position that was! I found b4!!, but I didn't see the ...Bg5! defense, which is the only thing that saved Black from an immediate crushing.

1 Rh5+! gh5 2 Ne5!! Rg8 3 Qe4+ and 4 Nf7!# the Ne5 move is essential to a avoid the pin of the white's Quin by black's

Yes.Though there seems to be a problem with my line since after 3 Qe4+ Rg6 4 Ng6 is a lost position.The best line I have found is one that leads to draw.So my moves did not have the correct order (it happens so often and with devastating results).After 1 Ne5! Qd4! 2 Rh5+ and now of course 2 ...Kg8 3 Rh8+ Kh8 4 Qh3+ Kg8 5 Qh6 and now black have the perpetual chech.I hope this is the correct one!I'm always open to sound lines :)

1Rh5+ gxh5 2.Qe4+Kh8 (Kg8 3Ne3 Qe3 4Qg2+ Qg3 5.hxg3 +- )3 Qf4 Qg1+ 4Kxg1 Rg8+5Kh1 Rg6b6 Ne3 +-

.f vertical is weak but open vertical..
1.Rxh5+,gh5
2.Ae4!,Rh8
3.Qe4+,Kh8 if 3.....,Kh6
4.Nf7# 4.Qd3,Rf5
5.Af7(+,-)

What about 3 ..Rg6, 4.Nxg6, Qe3? 5.Nf8 Kh6?
Perhaps 3. Qc2 is better..

Thanks for all the help! My naive Rxh5+ line got demolished and I can't find a win.

However, Qe4 seems to draw. My two main lines are
a) Rh8 Rxh5+ Kg8 Nh6+ Nh6+ Rxh6 Rxh6 Qc6 Qxc6 bc Rh4 == and
b) Kg8 Nh6+ Kh7 Nxf7+ Kg8 Nh6+ Kh8 Nf7++ etc.

Oops. Just realized will's line works when the typos (4...Rg8 is not check) are fixed. My problem with it was:

Rxh5+ gh Qe4+ Kh8 Qxf4 Qc6+ Kg1 Qc5+ Kf1 (Nf2? Rg8+) Qxc4+ Qxc4 hg but Qf4 still mates.

Ne5

Looks like immediate Rxh5 does not work. My line is:
1.Ne3! fe 2.Rxh5 Kg8 3.Rh8+ Kxh8 4.Qh3+ Kg8 5.Qh6 and 6.Qg7 mate
If 1... Qc6.2.Nd5 and 3.Rh5

Thanks Miranda!!!I insist on my choice for Ne5! and that white cannot go for more than a draw!The main refutation for the line of will and Amann Ross is that after 1Rh5+ gh5 2Qe4+ Kg8 3Ne3 black answers with the excellent move Qb2!!! the black queen protects g2 from a check and after Qf4 black answers Qe5 and it is over!!!Difficult position for someone that sees it for a first time and I wonder if it is not a study whether white and black found the correct answers!