Black to play and... lose

This rook ending arose in the game Wolff – Fishbein, USA Jr. Ch. 1988 and was analysed by Fishbein in Informant 47. Black will soon have to surrender his rook for White's advanced pawn, and his drawing chances will turn on whether he can promote his own pawn safely. Because it is still on its home square and White's pieces are not too far away, indications are that the race will be a close one. In the game Fishbein managed to achieve the draw as follows:

1...Kg5
Unavailing is 1...Rc1+ 2.Kd8 Kg5 3.Ra5+ Kg4 4.Rd5! (making it more difficult for Black to control the queening square) 4...Ra1 5.Ke7 Ra8 6.d8Q+ Rxd8 7.Rxd8 h5 8.Kf6 h4 9.Rd4+ Kg3 10.Kg5 h3 11.Rd3+ Kg2 12.Kg4 h2 13.Rd2+ Kg1 14.Kg3 h1N+ (or 14...h1Q 15.Rd1 mate) 15.Kf3 and wins.
2.d8Q+ Rxd8 3.Kxd8 h5 4.Ke7 h4!
Of course not 4...Kg4? 5.Kf6! h4 6.Ra4+ and White wins as in the previous note. In these positions the technique of “shouldering off” the opposing king always plays an important role.
5.Ke6 h3 6.Ke5 Kg4 7.Ke4 h2 8.Rh7 Kg3 9.Ke3 Kg2 10.Rxh2+ 1/2-1/2

Based on this rather straightforward result, the diagrammed position is labeled by Informant 47 as “Black to play and draw.” But it turns out there is a large and surprising improvement for White:

1...Kg5 2.Ra1!!
Black must of course avoid the capture, but the result is that White's rook gains crucial checking distance against Black's king.
2...Rd2 3.Rg1+! Kf5 4.Rh1! Kg6 5.d8Q
After some accurate play to restrain Black's king, White now cashes in his pawn for Black's rook. Meanwhile Black's pawn has still not moved.
5...Rxd8 6.Kxd8 h5 7.Ke7 Kg5 8.Ke6
White is obviously somewhat ahead of the game Wolff-Fishbein, and the difference is enough for a decisive result. Here is one possible conclusion:
8...h4 9.Ke5 Kg4 10.Ke4 Kg3 11.Ke3 h3 12.Rg1+ Kh2 13.Rg8! Kh1 14.Kf3 h2 15.Rb8 Kg1 16.Rb1 mate.

As they say, it just ain't over till it's over!