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This came to my attention on Chess Stack Exchange.

Geir, I'm sorry to say this, but I found out today that your 32 ply position is BUSTED: 10. Kf2 works as an alternative to 10. Kg2.

However, Stockfish analysis confirms that your 25 ply position is sound, and thus still the record.

White’s 9th move is Kxh1, so I am pretty sure 10.Kf2 is illegal. Otherwise I would agree that 10.Kf2 is a cook.

(43) Posted by Rewan Demontay (Real Name: James Malcom) [Tuesday, Jan 12, 2021 01:03]

Oh, my oh my! You're right, so it isn't busted. I accidentally swapped the king and the knight. My bad Geir!

I have found a way to make 20, 21 or 25 plies without captures. The number of plies depends on how you treat threefold repetitions.

(= 9+7 )

1.h7 Rd8 2.Bf7 Rh8 3.Bg8 Kb8 4.Kb1 Kc7 5.Kc1 Kd6 6.Kd1 Ke5 7.Ke1 Kf4 8.Kf1 Kg3 9.Kg1 Kh3 10.Kh1 Kg3 11.Kg1 Kh3 12.Kh1 Kg3 13.Kg1 draw.

The reason this is all forced is that White wins if he gets to play Kg2, while Black wins if he gets to play Kh2. With Kg2 vs Kg4, White plays a5 to put Black in zugzwang, but with Kf1 vs Kh2, the pawn move only serves to delay the zugzwang by one move.

The question now is how long this line is to be considered. If you count the moves before any position is repeated, that is 20 plies (10...Kg3). If you include the move that makes the first repeated position, that is 21 plies (11.Kg1). If you count the moves to the threefold repetition, that is 25 plies (13.Kg1).

My suggestion is that due to the theme, you should count
to the first unforced move of one side. And that would be the
automatic draw, for fuzzy values of "move" and "forced" :-)

Hope I’m not making a dumb error here, but it seems to me that in the 3Rep study, White is safe as soon as he plays 9. Kg1. At that point he can freely advance Pa4 without risking loss. So the sequence of Nunn single moves ends at 18. That pawn still served a purpose in that it stopped Black dawdling on the 4th rank.

9. Kg1 Kh3 10. a5 Kg3 11. Kf1 Kh2 B+ or 11. Kh1 Kf2 B+.

Thanks, Joost. Sorry I was remembering the board wrong when I was cycling. I will have another look maybe later today when I'm freer.

I just realized I can add two plies like this:

(= 9+7 )

1.Bh5 Rd1 2.h7 Rd8 etc.