The most beautiful puzzle that my engine can never solve

Your skillset appears to mostly consist of glibly repeating vague mantras and being abusive. Also incorrectly reasoning from quotes.

The skill you could do with developing is logical reasoning.

You don't seem to understand what a 1-ply analysis is. The position I posted showed analysis lines to many moves and a search depth of 26. That is NOT a 1 ply analysis. Note also, that you seem to forget that a 1-ply analysis generates a new set of positions without 1-ply analysis. At the extremes of an incomplete analysis tree, you always have a set of positions that do not have a 1-ply analysis. If every position has a 1-ply analysis, the analysis is complete, contrary to your fanatical belief.

The point was that the lines Stockfish was analysing in my example were the most extreme example of irrelevant, inferior lines possible. The idea that it would fail to permanently prune such lines but prune some other type of line is, to an intelligent person, obviously absurd.

One possibility you miss is that Stockfish can do its analysis, pruning low priority (or even strictly inferior, like in my example) lines, but later, when there is nothing better to do analyse those lines. That is what happens in my example, and that is what happens at every leaf node in the hypothetical end.

It is an interesting discovery that Stockfish does this even when it has categorically solved a problem - it has found the shortest mate, proved that there are no other alternative mates, and yet continues to analyse inferior lines. Because it can, and it has nothing better to do.

In our hypothetical case where Stockfish has no problems with computational resources, it does the same at every position in the analysis tree, each one being in the hash table so it is found if it is reached by transposition.

No, that is an answer a google search finds on Quora. It is from a contributor using the fake name "Alfred Alphazero". But it is correct if about a specific implementation of Stockfish, which can have say a maximum hash table size. Here is a more relevant answer from someone who uses his real name.

I want to learn more!

Whatever StockFish does or can do (are they different?) the underlying design principle is that reaching an end point (in time) has a higher priority than reaching an end position (game state). The point where SF could solve chess has long been passed because the price was too high - 200 billion years. Which is the fate of complex mathematics. You won't see it appear until it has been reduced and restricted and the tools are powerful enough to permit practical application - see ChatGPT.

Yes. There is a huge gap between the theoretical and the practical.

With AI, it wasn't so much that there was a theoretical demand, it's just that enormously increased computational power made a lot more possible. I was fascinated by neural networks in the dark ages (after they had been invented then went out of fashion while computationally cheaper alternatives had a lot of success. With 1000 times more computing resource (probably a million times with the big LLMs, which run on very powerful centralised hardware with stacks of state of the art TPUs), a lot more has been achieved.

The ChatGPT hardware has thousands of individual units suitable for interacting with individual users, each of which has 8 state of the art V100 TPUs. Each of those units is more powerful than the world's fastest supercomputer in 2004 - 800 teraflops.

If white moves first my engine took 10 seconds and depth 42 to realise white is winning

That is an amazing puzzle. I only got a few moves correct

2024, with Stockfish 16.1 this finally gets solved within seconds :-)

Congratulations 👏🎉