Why can't Stockfish solve this?

(this puzzle is from arves.org via Daniel Naroditsky YT) Here is really cool puzzle that would take me lifetime to solve.  White move and mates. This is well under 20 moves however Stockfish seems clueless until you make the first move. (spoiler, 1. Qc8!!) Had the depth set at Unlimited and still nada.  Any ideas why?

Why not gxh7?

1. gxh7 Qe5+  2. Kxe5 Kg7

If 1. Qc8 ... Kg8

Mine wins easily, no skill needed. Maybe mine is not as fast.

1...Qxd8+   It is a really cool solution.  I would run it in analysis or check out the site.  https://www.arves.org/arves/index.php/en/halloffame/84-mario-matous  That is not the point.  I'm really curious why stockfish can't solve it even if it's under the depth limit.

The solution must already be found. 

(I put answer of AI with black) 

1) gxh7-Qxd8+ 0-1

1) Qc8-Kg8 (if 2.gxh7+ Kh8) 

I think is fake, there is no mat for white so Stockfish can't find.

ok, here is the solution since clicking on the link seems to be difficult.  but back to my question, why can't stockfish find this?!?! its 13 moves which shouldn't be a problem.

edit; there is another line that mates in 9 that was missed.  but that makes it even stranger as to why the engine will not find it.

Woah is no fake. 

Otherwise the explanation is maybe similar as for the encirclements of the Queen not seen .

I.e. the program should stop its calculation [for a precise variant] because in its programmed data it gives a clear evaluation [indicating to stop its calculation]. 

Engines like SF don't exhaustively analyse every legal move for both sides up to a particular depth. Seemingly weak moves are "pruned" to improve efficiency, meaning it's possible for engines to overlook what is actually the best move. Hence it's not that rare for SF to fail to solve complex endgame studies like this one. Also, engines apparently can have trouble handling some complicated zugzwang situations, and this study has one of the most surprising zugzwang around.

The more interesting question for me is whether this study is actually unsound, as claimed by the ARVES site linked. That site is run by endgame experts, so it's generally safe to accept their analysis, but oddly I can't verify the supposed cook, 1.Qd6+, with engine help. Regardless of how SF can't solve the study, the engine is still useful to check whether a given variation is correct. Thus when the first few moves of the intended solution are played – 1.Qc8! Kg8 2.Bc7!! – the engine suddenly sees that White has a forced +M11 against the best defence, 2...Qxc8, i.e. the queen sac is indeed sound.

But consider the claimed cook, 1.Qd6+ Kg8 2.gxh7+ Kh8 3.Be7. The ARVES analysis gives three sub variations, for 3...Qc8, 3...Nc7, and 3...Nb6, the first two of which do win for White according to SF. However, the engine thinks 3...Nb6 4.Qxb6 Qa8 5.Qb3 Qg2! (not 5...a4 as per ARVES) is a draw, and in fact it prefers 3...Qb5 as the best drawing defence (eval 0.00 after an hour), not mentioned by ARVES at all. I manually tested a few reasonable white replies, such as 4.Qd8+ Kxh7, and then both 5.Qxa8 and 5.Kxf7 are tablebase draws. (I also tested this 3...Qb5 position with a problem-solver that finds all short mates and there's definitely no forced mate in 10 moves or fewer for White.)

Therefore I think 1.Qd6+ doesn't win and the original brilliant study by Matous (with the queen starting on a6) is correct with one solution, 1.Qc8!

Why no centar tournaments?

GMs enter lines into the computer, which then investigates those deeper than it might otherwise, in addition to its regular search?

Magnus and Stockfish vs Hikaru and Komodo?

Some masters or experts who know the weaknesses of computers and have uneven skills tactically vs positionally might do well in such centar tournanents.

Ugh, why would you spoil the answer right in the question??? =/

@Rocky64 Thanks for the insightful answer.  I guess the question then is, who does the pruning?  I also thought that the whole point of an engine is to run through all the possibilities, and therefore the depth limit.  Thanks again!

Did Qc8 really ruined it for you tho?  The question wasn't really about the solution and was hoping to steer away from that convo.

At depth 68 my Stockfish 15 says white is clearly winning, and at depth 80 something it already says mate in #13. You just have to be patient and wait it out.

 It's worth noting someone has already run through this very same position before, as you can see by the online position analysis. Another engine, Fritz 17, still considered it 0.0 at depth 52. 

No worries! Pruning is programmed into engines like SF by their creators because it actually improves their performance and ratings. Modified engines that don't prune, like the one mentioned by @pfren, are great at solving complex studies, but are weaker than the standard pruning versions in the practical game, presumably because they waste time analysing "bad" moves. Programmers probably run test matches between these different types of engines and the non-pruning ones would end up with a lower score and rating.   

Pruning is necessary because every half move multiplies the number of games by 30 or so. That's 1000 for each full move, a billion for 3 fulll moves. Can your computer process trillions of positions? If not, it can't do 4 full moves deep. Hence pruning.

But pruning sometimes misses the best moves.