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1st Prize Winning Study From StrateGems

1q2brk1/4b1p1/1r4B1/p3N3/5P1N/2pP1R2/6P1/4Q2K w - - 0 1

This was one of the three compositions that shared 1st Prize at StrateGems 2017. While this is a beautiful study, I do have issues with it deep within the solution (at move 12 for black in the main line). I can't convince myself that white wins in some of the possible variations, so am putting the problem up to see what others think. So, if you find the main line, please feel free to use a chess engine to analyze the position after white's 12th move, since I would like to have an answer I can trust about those variations.

V-1

1.Rh3! Rb1
2.Bh7+ Kxh7
3.Nhg6+ Bh4
4.Rxh4+ Kg8
5.Rh8#

V-2

1.Rh3 Bxg6
2.Nhxg6 Rxg6
3.Nxg6 Qd6
4.Nxf8 c2
5.Qc3 Kxf8
6.Qxc2 Qd7
7.Rh8+ Kf7
8.Qc4+ Kg6
9.Ra8 Bb4
10.Kh2 Bd2
11.Ra6+ Kh7
12.Qe4+ Kg8
13.f5 Kf8
14.Ra8+ Kf7
15.Qc4+ Ke7
16.Qh4+ Kf7
17.Qh5+ Ke7
18.Qe2+ Kf7
19.Qxd2

V-3

1.Rh3 Bd7!

I haven't solved V-3 yet. I got only a draw so far.

V-3 is the main line.

V-3

1.Rh3! Bd7!
2.Bh7+ Kxh7
3.Qe4+ Kg8
4.Qc4+ Kh7
5.Qe6! Rb1
6.Kh2 Rh1+
7.Kxh1 Qb1+
8.Kh2 Qg1+
9.Kxg1 Bc5+
10.d4 Bxe6
11.f5 Bxd4+
12.Kh1 Bxe5
13.Ng6+ Kg8
14.Rh8+ Kf7
15.Rxf8#

cool move Rh3, is it possible to reduce V-3 to this?
1.Rh3 Bd7 2.Bh7+ Kxh7 (...Kh8 3.Nhg6#) 3.Nf5+ Bh4 (...Kg8 4.Nxe7#) 4.Rxh4+ Kg8 5.Ne7#
oops forget that I missed 3...Rh6 is possible

(edited)

Alena, well done- you found the mainline Krug gives in his solution. My issues are at move 12 for black- it isn't so clear cut a solution if black plays 12......g6 or especially 12.......g5 instead of the mating line that arises after 12.......Bxe5. It looks like white wins in those alternate variations, but I can't prove it.

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