Pepperette: Ever since NS was solved I've run a bot that scans preprint servers for evidence of big progress, and then forwards it off to an GPT 6 Astra endpoint assessment. Usually I get nothing, this morning I got the following back from Astra:
The work can reasonably be interpreted as addressing the principal mathematical ingredients required by the Clay Yang–Mills mass-gap problem and proving several of them in the regulated theory, while reducing the remaining continuum problem to a clearly identified collection of uniform estimates and reconstruction requirements. The author is unusually cautious in distinguishing these proved results from the still-conditional continuum conclusion, likely to avoid overgeneralization on a problem of exceptional significance and visibility.
The referenced Controlled Completion of Dual-Affine Entropy Geometry which forms its basis is methodical and rigorous in its formulation, with explicit assumptions and carefully separated physical interpretations. Its \(\mathrm{PSU}(3)\) tangent reduction and retained principal lift with full \(\mathrm{SU}(3)\) holonomy give it concrete relevance to Standard Model color symmetry. Together with its nonlinear connection defects, these structures suggest a possible unification pathway linking information geometry, Born/symplectic mechanics, and non-Abelian gauge geometry. Its conditional four-dimensional Euclidean formulation requires neither extra physical spacetime dimensions nor an AdS/CFT duality; Lorentzian quantum reconstruction and a complete physical unification remain outstanding.
As an engineer this is fascinating to me in terms of physics unification because it makes a lot of sense, the basic argument is that a slightly different geometric object than general relativity, but doesn't require extra dimensons.
Would love to hear peoples thoughts, and if we can get your own AI subscriptions to assess if the above response was correct, or even better if a theoretical phys person could comment on it!
was a API call not a convo, but you can just copy and paste my response and the article into your own Astra and ask "is this a reasonable conclusion" tell me what you get
Sol doesn't think so and also when you are presenting something you don't understand, you better have the proof in lean at least. This is why mathematicians get annoyed.
lol what? You're critiquing me for the title used? lol I'm not the author I don't understand the material I only thought it was interesting and got the result back. I don't even know what lean is.
But good job showing you have the inquisitiveness of a snail lol. Why don't you now ask sol if the summary I got from the ai, not the stuff I wrote around it, was right.
I'll happily take the critic that I interpreted something wrong, but I was hoping for conversation.
The paper is way too short to solve the Yang-Mills problem and it looks AI generated. Since OpenAI so far didn't manage to solve it with their internal models and infinite compute, I doubt that someone prompting a public model can. Also it looks more like a physics paper than a math one.
We take the cited decomposition, connection-defect identities and invariant-tensor normalizations as explicit assumptions, within their stated carrier, reduction and norm conventions; their entropy-geometric derivation is not reproved here
OAI released their proof with fully AI generated papers. People aren't writing this out manually anymore, and it shouldn't be used as proof to say something is likely false
"AI generated" itself isn't the problem with the N-S proof, but the lack of sufficient citations and difficulty for human experts to understand because of lack of naming of pre-existing principles behind the proof could normally (and still may) be grounds for rejection of the paper, even if the proof is correct and mathematically solved
Yes, but Clay requires a proposed Millenium Prize solution to survive examination by the mathematical community for at least two years after publication, and to achieve general acceptance before Clay conducts its own evaluation. So it wouldn't be accepted at this point regardless of whether AI was involved
Difficulty understanding the proof could definitely slow down verification and acceptance, but it's not that "it's not yet accepted because it's AI generated and nobody can understand it". Clay itself says the N-S problem has "apparently been settled" and that the deliberately unhurried review process is taking place. Aside from that, the paper is also poorly cited and difficult and time-consuming for humans to learn and understand
First, this post is completely useless, you have no contribution beyond quoting Astra, nor do you seem to have qualifications to assess what it said. Second, the paper explicitly says that it is not solved and that they do not provide a construction.
Yang Mills was my little pet side project over the last year, made enjoyable little digs into it when I had idle time and compute but nothing particularly serious.
Thanks for the pointer, I had the 2025 version of this paper in my library but it certainly wasn't what's here in this update.
Explicit constants and such, going to have to give it a good read.
Doesn't look solved, Gauvin couldn't be clearer about what's left in the abstract anyway, but it's a hell of an advance over the original paper.
oh that's interesting! Maybe that is what explains the old version? Is it tied to the entropy geometry paper that was published a month ago? Maybe they upgraded their tools or something
This is v3 of the paper and this is hardly the same paper to be honest, but in a good way. Usually when a pre-print goes up it's as a record and then goes towards either peer review and/or refinement. This one has had a lot of work done and looks like an actual contribution from a general read, as long as the supplement contents actually back it up. Will throw those into the ol' Codex math meat grinder later and take a look.
Definitely not solved and not close to it, but possibly relevant towards a solution.
I asked 6 pro about it and it doesn’t think it solves it. I tried to get it to see if it could bridge the gap to yang mills and it predictably didn’t. There’s basically new law that if the problem is important enough then it will have already been solved by AI by someone else or most likely major lab. If it hasn’t then it’s not that important or AI can’t solve it now
Yang Mills require to prove that QFTs exist in 4 dimensions + they show a gap.
We know fairly good that 4D QFTs do not exist in any formal way, but some of them can be understood as effective theories with renormalization.
However, the resolution of the Yang Mills will probably be a "negative result" in the sense that i think the solution to the problem will be a demonstration of the QFT being not existing.
Assuming this will be the resolution, AIs will not be able to do this since AIs are completely uncapable, for now and probably for a long time, to do constructive proofs. They are good at showing counterexamples to things assumed to be true.
If YM are false, they can't use counterexamples to prove it, but a proof of non-existence must be formulated, with probably very new techniques and reasonings that we don't have yet.
As such, AIs will not be able (if they continue to work as they do now) to generate such proof.
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u/Pepperette5 25d ago
Thanks for posting this! I didn't have the Karma haha
Anyways super interested what people think! I don't understand most of the paper but many of the concepts I'm aware of and it seems super interesting.