A Homological Proof of P != NP: Computational Topology via Categorical Framework
1–10 of 22 posts
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#2I'm not sure if this is real, but the abstract says machine-verified.
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#3I'm not sure if this is real, but the abstract says machine-verified.
For a claim this big, I'm surprised only one author. Not even an advisor?
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#4Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#5Earlier quoted context omitted.
For a claim this big, I'm surprised only one author. Not even an advisor?
Once upon a time, people published solo often. It's just harder to do things like that these days.
In the last few months, I've seen a proof of P=/!=NP every two weeks in /newest, so color me skeptic.
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#6The paper seems to make no mention of the natural proof barrier, so it is almost certainly not a proof of what it claims
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#7I'm not sure if this is real, but the abstract says machine-verified.
Pg. 56 cites this repository which is either still private or doesn't exist:
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#8The GitHub repo 404’s and likewise with the Docker image. Where's the code?
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#9I'm not sure if this is real, but the abstract says machine-verified.
Yes. From a quick scan of the paper, it includes a formal proof in Lean4. That said, it is very long and complicated, with lots of steps in the chain (as you might expect) so it would need to be checked carefully to ensure it proves what it claims to prove.
Lean uses Curry-Howard correspondence, so how proofs work is you declare your propositions as types and then your proof is actually a recipe that goes from things that have already been established and finishes by instantiating that type. The guarantees there are very strong - if you succeed in instantiating the type you have definitely proved something. The question is whether you have proved the thing you said you have. So here scanning the proof (it’s like 100 pages and I am sick so definitely sub-par intellectually) they use category theory to embed the problem, so the proof is actually a proof of the properties of this embedding. So if there is a problem with the proof, my guess would be that it would lie in the embedding not being exactly representative of the problem somehow.
It seems a pretty serious attempt though- it’s not just some random crank paper.
Re: A Homological Proof of P != NP: Computational Topology via Categorical Framework
#10The paper seems to make no mention of the natural proof barrier, so it is almost certainly not a proof of what it claims
what's the natural proof barrier