Chess will never be solved, here's why

1. Is underpromotion ever the sole best move in a competitive chess game?

Yes

2. Is there some N such that the existence of N previous underpromotions in a line safely implies that underpromotion is not the sole best move?

No

Consequence: no underpromotion can be neglected on the basis of a zero ply analysis, as you suggest.

@10858

"any thought processes nor any arguments" ++ Capablanca mentions that 1 e4 and 1 d4 open diagonals for the bishop and queen. 1 e4 and 1 d4 also control the center. 1 a4 does neither.
AlphaZero ranks 1 d4, 1 e4, 1 Nf3 as top 3 and 1 a4 as #13 of the 20 legal first white moves.
The ICCF World Championship Finalists play 1 d4 most, then 1 e4, then Nf3, nothing else.
"completely unknown waters"
++ That might be an argument for a blitz game, but not for the ICCF World Championship Finals. After 1 e4 or 1 d4 black must work to draw, after 1 a4 white must work to draw.

@10862

"1. Is underpromotion ever the sole best move in a competitive chess game? Yes" ++ Correct.

"1. Is there some N such that the existence of N previous underpromotions in a line safely implies that underpromotion is not the sole best move? No" ++ That is besides the point.

"no underpromotion can be neglected on the basis of a zero ply analysis" ++ Yes.
Look at the 3 random samples.
First position: 7 white rooks, 3 black bishops. Underpromotion to a rook or bishop instead of a queen can only be optimal play to avoid a draw by stalemate. It makes no sense for both sides to avoid a draw. Hence the position cannot result from optimal play by both sides.
Second position: 4 white rooks, 2 black dark square bishops.
Same argument: cannot result from optimal play by both sides.
Third position: 4 white rooks, 3 black rooks.
Same argument: cannot result from optimal play by both sides.

@10864

"ALL LEGAL MOVES FOR THE OPPONENT NEED TO BE EXPLICITLY ANALYSED BECAUSE A ZERO PLY EVALUATION CANNOT BE RELIED UPON"
++ NO. IT IS BENEFICIAL TO INCORPORATE GAME KNOWLEDGE IN SOLVING A GAME.
IT IS ALLOWED TO APPLY LOGIC IN SOLVING A GAME.
SOLVING A GAME DOES NOT REQUIRE TO SHUT OFF THE BRAIN.

"solution of checkers, which took over 1000 years of CPU time"
++ Mostly for generating the endgame table base.
We already have a 7-men endgame table base for Chess.
Besides 17 finalists * 16 engines/finalist * 2 years = 544 years of CPU time,
anno 2024, more powerful CPU than Schaeffer 2007.

@10867

"why 106 out of 106 does anything at all regarding Svesnikov's pronouncements"
++ They now do what he said:
'I will bring all openings to technical endgames and weakly solve chess'
They are the good assistants, and their computers are the modern computers he asked for.

@10869

"in your insignificant number of examples"
++ The 3 random samples are representative for the 10^44 legal positions.
They all look like that.
There are only 10^37 legal positions without promotions to pieces not previously captured.
That is 1 in 10^7.

"In principle it can be that later it would be impossible to mate"
++ It cannot be optimal for both sides to avoid a draw by stalemate.

"you need to exclude ALL underpromotions"
++ Gourion excludes all promotions to pieces not previously captured.
That is too restrictive, hence *10 to include 3 or 4 queens.
Inspection of a random sample of 10,000 positions without promotions to pieces not previously captured reveals none can result from optimal play by both sides, hence / 10,000.
10^37 * 10 / 10,000 = 10^34
Sqrt (10^34) = 10^17 for weakly solving

@10866

"I don't think that 1. a4 damages white's position." ++ White can still draw.

"1. a3 is stronger" ++ Yes. AlphaZero ranks 1 a3 #10 and 1 a4 #13.
1 a4 weakens square b4, while 1 a3 strengthens it.
E.g. 1 a4 e5 2 e4 Nf6 3 Nc3 Bb4, while 1 a3 e5 2 e4 Nf6 3 Nc3 interdicts 3...Bb4.

You are like someone who turns up at a chess tournament and tries to argue that his table tennis serves will ensure he wins.

Translation: I have given up on my premise, and this is all I have left.

After years of everyone telling you your premise falls apart, you have decided to lower the bar to what actually exists now, and calling Sveshnikov's work ergo done. It's a weak capitulation, and obviously not "solving chess" at all.

Your instinct based on a week or two of *other* people saying that 106 draws does not prove anything...you're welcome.

@10876

"you and Elroch are using contrasting, working definitions"
++ I think we agree on the Van den Herik definition, but Elroch has a puristic interpretation of it.

He's not lying. Tygxc and Optimissed are daft and doddering, respectively. Optmissed is here arguing about Tygxc's process of fudging his way down to 10^17. This process has been refuted dozens of times in this thread. Optimissed does not remember things for very long (except his stories), and is re-inventing the wheel (something he often does, while claiming he just came up with something). Tygxc's reduction from 10^44 to 10^17 does not work. That's the whole reason Tygxc is pushing the ICCF and the 106 draws now...because his numbers don't work, so he is moving the goalposts. Optimissed is just floundering along as he usually does in these type of threads...tossing in nonsense or restating the obvious and then claiming he rules the discussion...it's nothing new, he's been doing it for 10 years...but his memory is getting worse over time. Thus the claims about "you've never said this", "I figured this out myself", etc.

There used to be a third crackpot, Ponz, who faded into the sunset years ago. The difference was, Ponz was a former US correspondence chess champion, and had some credentials for posting the premise that chess is a forced draw, but he had dementia (self-admitted) and his reasoning became much like you see here with Tygxc and Optimissed...incessantly repeating a bunch of stuff that proves nothing in the end.

I think you mean a correct interpretation of it.

No the opposite

There are a infinite number of infinities, and each is infinitly bigger then the last.

what the f**K does that even mean

You seem to have wandered out of your corral.

What i dont understand is someone can make predictions about what increased computer power might discover in a 100 years?

It might be that being white being the first to move actualy is a zugzwang where black can win by just following a matrix regardless of what white does.