"and it retroactively validates all black moves as optimal by the authority of the table base."
No it doesn't.
...
Exactly.
Thank you Martin !
Well, it might if, by some immense stroke of chance, each move by the black side turned out to be optimal, even though an undirected guess.
And - whether the 50 move rule is invoked or not -
it will not change the uniqueness of any chess position.
...
Of course it will.
Try mating from this position on the analysis board.
We'll disagree on that one Martin -
but you might 'get me' on how I worded it ! 
I should could would have said - 'uniqueness on the board'.
Qualification.
Too late !
@playerafar
A position with e.p. and a position with not e.p. is still uniqueness on the board if they have the same diagram. Chess works by positions, not diagrams.
@tygxc's proposed "solution" uses SF14 which evaluates positions differently depending on the ply count.
The 50 move rule does not and cannot alter the fact that chess may be (very hypothetically) a forced win from the starting position, which would invoke that rule if the rule were in place. Any true solution of chess ignores the 50 move rule. Otherwise, it is not a true solution of chess.
It's best not to define things using words which also have to be defined. "Uniqueness" has a unique meaning .... that there is only one such existing. If such a word has to be especially defined, meaning that there may be some ambiguity, then use a different way of explaining.
@tyxgc
Just realised why you were asking if I could find a position where Stockfish's first four evaluations were all wrong.
As I already said, it's not relevant, but it is quite easy.
This is an 8 second evaluation (time which gave the lowest blunder rate in the KNNKP position I posted earlier).
The only move to win in either game is ...Qg2+
The 50 move rule does not and cannot alter the fact that chess may be (very hypothetically) a forced win from the starting position, which would invoke that rule if the rule were in place. Any true solution of chess ignores the 50 move rule. Otherwise, it is not a true solution of chess.
FIDE defines two different games, both called "chess". Either may be solved (the competition rules game with some assumptions about clocks and arbiters). Any strong solutions will be different, as, almost certainly, will be any weak solutions.
It's best not to define things using words which also have to be defined. "Uniqueness" has a unique meaning .... that there is only one such existing. If such a word has to be especially defined, meaning that there may be some ambiguity, then use a different way of explaining.
I assumed by uniqueness @playerafar was referring to a unique position corresponding to a diagram and side to play. Why do you see an ambiguity?
The 50 move rule does not and cannot alter the fact that chess may be (very hypothetically) a forced win from the starting position, which would invoke that rule if the rule were in place. Any true solution of chess ignores the 50 move rule. Otherwise, it is not a true solution of chess.
FIDE define two different games, both called "chess". Either may be solved (the competition rules game with some assumptions about clocks and arbiters). Any strong solutions will be different, as, almost certainly, will be any weak solutions.
It's best not to define things using words which also have to be defined. "Uniqueness" has a unique meaning .... that there is only one such existing. If such a word has to be especially defined, meaning that there may be some ambiguity, then use a different way of explaining.
I assumed by uniqueness @playerafar was referring to a unique position corresponding to a diagram and side to play. Why do you see an ambiguity?
Firstly, if "strong" and "weak" solutions differ from each other then they are not solutions, in the proper meaning of the word. They're just something mysterious and rather meaningless, to which some people choose to attach relevance.
There's ambiguity because you implied that there are positions you call unique but which aren't unique because en passant rights may have been lost or retained. At least, that's the impression you gave.
So's almost everyone. They're quite good at it.
The 50 move rule does not and cannot alter the fact that chess may be (very hypothetically) a forced win from the starting position, which would invoke that rule if the rule were in place. Any true solution of chess ignores the 50 move rule. Otherwise, it is not a true solution of chess.
FIDE define two different games, both called "chess". Either may be solved (the competition rules game with some assumptions about clocks and arbiters). Any strong solutions will be different, as, almost certainly, will be any weak solutions.
It's best not to define things using words which also have to be defined. "Uniqueness" has a unique meaning .... that there is only one such existing. If such a word has to be especially defined, meaning that there may be some ambiguity, then use a different way of explaining.
I assumed by uniqueness @playerafar was referring to a unique position corresponding to a diagram and side to play. Why do you see an ambiguity?
Firstly, if "strong" and "weak" solutions differ from each other then they are not solutions, in the proper meaning of the word. They're just something mysterious and rather meaningless, to which some people choose to attach relevance.
Well that's just a matter of you finding out what the topic's about. As @Elroch already suggested - try Google.
There's ambiguity because you implied that there are positions you call unique but which aren't unique because en passant rights may have been lost or retained. At least, that's the impression you gave.
I pointed out that positions with the same diagram and side to play but different ply counts are not unique in exactly the same way that positions with the same diagram and side to play but with different e.p. possibilities are not unique. I didn't call anything unique.
#1960
"Can you make up your mind what game you're proposing to solve, please?"
++ Laws of Chess, but without the 50-moves rule.
The 3-fold repetition rule stays and could even be simplified to a 2-fold repetition rule.
"If you read the post you will see that SF14's blunder rate doesn't improve with increased think time, rather the opposite."
++ OK, but your longest thinking time is still short and your hardware inferior.
"If you give SF14 60 hours/move on a 10^9 nodes/s cloud engine it could well turn out to be little more than a random legal move generator."
++ I disagree. At 60 h / move and 10^9 nodes / s it goes right through to checkmate.
"I didn't look at SF14's alternative evaluations. What's the relevance? It plays the top move."
++ So the top move was an error. Was the top 2 move correct or an error too? Was the top 3 move correct or an error too? Was the top 4 move correct or an error too? I do not depend on the top move only. I run through 3 verification passes where I retract all white moves one by one and replace them with the top 2 move. If it is still a draw, then I retract all white moves again and replace them with the top 3 move. If it is still a draw, then I retract all white moves again and replace them with the top 4 moves. If it is still a draw, then I conclude it solved.
Chess is about mistakes so a computer solving Chess has no bearing on humans. We will still play Chess and we will continue to make mistakes.
Exactly
#1980
"Chess is about mistakes so a computer solving Chess has no bearing on humans. We will still play Chess and we will continue to make mistakes."
++ Yes, we probably will still play chess, but less so at top level.
Yes, chess is about mistakes, but we will make less mistakes after a solution is available.
So yes, it will have a bearing on humans.
Solved games like Connect Four, Nine Men's Morris, Checkers, Losing Chess are played both less and better than before they were solved.
#1963
"You said you were going to start with ECO 70. Which particular 26 man position would that be?"
++ No, I would not start with ECO C70, I would start with ECO C67. There will be more than 1 26-men tabiya per ECO code. The main 26-men tabiya for C67 would be this one:
"I would be interested if you could post your algorithm for determining your candidate moves."
Step 1: the 'good assistants' with ChessBase identify the most promising 50 ECO codes and prepare the relevant 26-men tabiya.
Step 2: Stockfish plays that position against itself at 60 h/move until it reaches the 7-men endgame table base or the game ends otherwise e.g. by 3-fold (or 2-fold) repetition, or stalemate. For each white move store the top 2, top 3, and top 4 moves for later reference.
Step 3: Lookup in the 7-men endgame table base that it is indeed a draw. We now have a candidate ideal game.
Step 4: Replace the last white move by the top 2 move and verify it is still a draw. Replace the last white move by the top 3 move and verify it is still a draw. Replace the last white move by the top 4 move and verify it is still a draw. Now replace the second to last white move by consecutively the top 2, top 3, top 4 moves and verify it is still a draw. Now 3rd to last move, 4th to last move all the way back to the tabiya. If all of these are draws, then it is proven that white cannot win the tabiya and that black can draw the tabiya and thus it is proven that the tabiya is a draw, with ideal games with optimal moves as evidence.
Step 5: Now repeat the procedure for the other tabiya of the same ECO code. If all of these are draw, then it is proven that the ECO code is a draw, with ideal games with optimal moves as evidence.
Step 6: Now repeat the procedure for the other selected ECO codes. If all of these are draw, then it is proven that chess is a draw, with optimal games with optimal moves as evidence.
Output: The output could be a book with 50 chapters one per investigated ECO code, each containing say 200 ideal games with optimal moves, all ending in draws.
[snip]
Output: The output could be a book with 50 chapters one per investigated ECO code, each containing say 200 ideal games with optimal moves, all ending in draws.
Yes, you could create such a book...you just can't call it anything close to a solution for chess.
And - whether the 50 move rule is invoked or not -
it will not change the uniqueness of any chess position.
...
Of course it will.
Try mating from this position on the analysis board.