So - I understand that there is a winning move for white?
Endgame Problem[very hard]
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Ok, let's see how many mistakes I made. My idea would be to first attack b4, forcing black to a5 (it looks like I win the race if he tries to go to the kingside). Then I march all the way to h5 (in the meantime he reaches g7), then I push g6 and I try to gain the opposition. Hope it makes sense.
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I see, it's a mess. I thought of something else but it doesn't work either. Have to think more about this...
I think now that the key is that white king has to be in d3, with black king in a6 *and* black to move. In that case black has to go b5 (or a5) and then white can win the race to go to h5. But it is hard to find the right way to reach this position (assuming that's the right way of doing it)...
Ok, I try again.
It looks like the corresponding squares are something like that:
1. White K in d3, black K in a6, and white wins if black has to move
(because black has to go b5 and white wins the race on the other side)
2. White K in e2, black K in b7, and W wins if B has to move
(because either black goes to a6, followed by Kd3 and we are in case 1, or black goes to h2, and white runs to the kingside)
...which should imply also the pairs c2-b7 and d2-h2, which in turn implies c1-b8 and d1-a8.
So maybe we can win with 1. Kb1 (maybe...)
White to play, try to solve it!