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Challenging Puzzle

Can you find white's winning plan here?

8/kP6/P7/1p1r2p1/pP2n1K1/3B2p1/p2R1p2/2r1R1Q1 w - - 0 1

I didn't find the first 6 or so moves in this puzzle difficult to find, but it gets much more challenging after that point. I am not even sure right now that the puzzle is valid and am still working out the details and verifying them myself.

Just to give you a bit of a hint, it is easy to see the main line the composer wanted you to find- black can force white into an underpromotion at one point that leads to a cute mate, but there were alternatives to that line that can't be easily discounted at a glance.

V-1

1.Qxg3 Nf6+
2.Kf3 fxe1=N+
3.Ke2 Nd7
4.Qe3+ Kxa6
5.Bxb5+ Rxb5
6.Rxa2 Rc2+
7.Rxc2 Nxc2
8.Qe6+ Kxb7
9.Qxd7+ Kb6
10.Qe6+ Ka7
11.Qc4 Rxb4
12.Qxc2 Ka6
13.Qg6+ Kb5
14.Qxg5+ Kc4
15.Qc1+ Kd4
16.Kd2 Kd5
17.Qc3 Rf4
It's a winning position for white.

V-2

1.Qxg3 Nf6+
2.Kf3 fxe1=N+
3.Ke2 Nd7
4.Qe3+ Kxa6
5.Bxb5+ Rxb5
6.Rxa2 Rc2+
7.Rxc2 Nxc2
8.Qe6+ Kxb7
9.Qxd7+ Kb6
10.Qe6+ Ka7
11.Qc4 Na3
12.Qc3 Nc2
13.Qxc2 Rxb4
14.Qh7+ Ka6
15.Qg6+ Kb5
16.Qxg5+ Kc4
It's a winning position for white.

I'm not good at queen vs rook endings at all. I need to study these endings( V-1 and V-2) to fully understand how to win.

The main line has black responding to 8.Qe6+ with 8......Nb6.

I will take a deeper look at the work after 8.....Kxb7 later when I have more time- this is actually one of the lines I am having trouble resolving thoroughly.

I have been able to reduce most the variations to similar Q vs R+P endings that I can, at least verify as won for white using Nalimov, but not all of them yet.

V-3

1.Qxg3 Nf6+
2.Kf3 fxe1=N+
3.Ke2 Nd7
4.Qe3+ Kxa6
5.Bxb5+ Rxb5
6.Rxa2 Rc2+
7.Rxc2 Nxc2
8.Qe6+ Nb6
9.Qc8 Nxc8
10.bxc8=Q+ Kb6
11.Qxc2 Rxb4
12.Qg6+ Kb5
13.Qxg5+

It's a winning position for white but I need to use Nalimov tablebase to understand how to win it.

What about 9.......Nxb4 instead of 9......Nxc8. I only ask because it is the main line the composer wanted you to find.

V-3(A)

9.Qc8 Nxb4
10.b8=N+ Ka5
11.Qa6+ Nxa6
12.Nc6#

V-3(B)

9.Qc8 Nxb4
10.b8=N+ Ka7
11.Qc7+ Ka8
12.Nc6 Nxc6
13.Qxc6+ Ka7
14.Qxb5 g4
15.Kf1 g3
16.Kg2 Kb7
17.Kxg3
It's a winning position for white.

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