Been pushing pieces around on my board for a good hour & I've come around to the idea that white can win this but not in the middle of the board & only from one starting position.
If black makes the mistake of landing on c6 when white's king is on e4, then white has to set off up the h-file & it will arrive at h6 before black can stop it. Then it captures the f6 pawn & is able to promote the f5 pawn a full 2 moves ahead of black (or at least one).
If black goes after white's f4 pawn instead, then white can use the a5 pawn move at the last moment to switch tempo from black & still capture the f6 pawn.
If the two kings remain in the middle, then it's a draw.
Here's my poor attempt at a diagram:-
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It all depends on which square the black king is sitting: c6 & black loses the game but d6 & it can force a draw. The critical square for white to reach is h6.
From your diagram, 1.Kf3 Kd5! 2.Kg4 Ke4 =
Been pushing pieces around on my board for a good hour & I've come around to the idea that white can win this but not in the middle of the board & only from one starting position.
If black makes the mistake of landing on c6 when white's king is on e4, then white has to set off up the h-file & it will arrive at h6 before black can stop it. Then it captures the f6 pawn & is able to promote the f5 pawn a full 2 moves ahead of black (or at least one).
If black goes after white's f4 pawn instead, then white can use the a5 pawn move at the last moment to switch tempo from black & still capture the f6 pawn.
If the two kings remain in the middle, then it's a draw.
Here's my poor attempt at a diagram:-
.
It all depends on which square the black king is sitting: c6 & black loses the game but d6 & it can force a draw. The critical square for white to reach is h6.