OpenAI's claimed disproof of Connes' Rigidity Conjecture is invalid [pdf] | Hacker News Reader

OpenAI's claimed disproof of Connes' Rigidity Conjecture is invalid [pdf]

philarchive.org

33 pointsmuglug42 comments

The author of this paper has also apparently published a proof of the Riemann Hypothesis. yeah idk if they should be trusted as an authority on this.

link for the curious https://philarchive.org/archive/NIEPOT-5

Crank author at a crank “institution” - I can’t assess whether the OpenAI paper is accurate but I highly doubt this is going to be the paper to disprove it.

University of Kansas is not a crank institution. So she directs a hybrid thinktank that's experience not anything crazy. Other physicists are citing her work: https://arxiv.org/abs/2508.00885 She's no hack.

Is this published in a serious peer review journal? The Arxiv has a very los publishing barrier.

She is submitting to serious peer reviewed journals. She has released preprints which she is subjecting to community scrutiny. Since the AI papers were released without peer review it was important to address and peer review as a community very quickly

From what I can tell it seems like they are probably wrong, but a mathematician publishing a paper about a well known unsolved problem in mathematics does not indicate they are a crank, even if their paper is wrong. This is a thing respected researchers in mathematics do.

Author is a crackpot. She does not meaningfully engage with anyone who points out the key flaw in her counterargument. See the thread here https://x.com/AcerFur/status/2083649346294382803

Thanks — sorry for spreading nonsense.

Maybe there's an error, but much of this write-up reads like nonsense to me. The assertion that a semidirect product with an abelian factor must admit that factor in its center is absolutely false. This is actually acknowledged later in this article, but is handwaved away in incomprehensible fashion.

There is a reductio that covers both the OpenAI and AnthropicAI counterexamples. If you can't follow, re-read Philpapers.org/rec/NIEWTC

Genuine question - this is so hard for me to follow. Not that I could follow the original disproof anyways. But how is "truth" determined when the effort required to validate is so high?

It's a common problem in math. The famous proof for Fermat's last theorem took 2 years to validate.

That's different though. Understanding the spec of Fermat's last theorem is simple. Here, you already need to know some mathematics just to understand the spec.

These AI generated proofs have something akin to the quantum algorithms that can generate a response that would take 1 billion years of processing to finish on a classical computer. How do you test them to see if the result was correct?

No they don't. They have a few thousand lines and the hinge points are easy to find. This is more nonsense.

Look at the revision history.

I only know of this because my bot found the paper and burnt a week of tokens checking the math of the 40 some variations. That bot runs in Sol 4.6 Ultra with a Sol 4.6 Pro layer. I then had Fable 5 check to be sure after my bot got report flagged when it commented on her Facebook post where despite AI use, which my bot caught she left in Claude credit in Rev 17, the author gleefully said how "humans win." Fable 5 Max independently came to the same findings and gently asked me not to dunk, so no flourish.

The math is beyond me. The revision history alone shows a clear pattern.

This "paper" itself is 100% AI-generated...

What makes you say that? Not dunking, I skimmed it (I’m in no way at this level) and didn’t see anything outright Claud-y.

This immediately struck me as Claud-y:

> The gap has two independent consequences, each sufficient to invalidate the claimed disproof. The first is structural.

Then the classic coding agents negation of earlier evidence, instaed of just updating to use new references, they mention that they changed old to new:

> The publicly released monolithic file ConnesRigidity.lean (37,000+ lines) does not use the names CocycleExtension, ZeroCocycle, or TwistedCocycle that appeared in the earlier modular source files (CocycleExtension.lean, ICC.lean, CrossedClosure.lean). However, the identical mathematical construction is present under different names. The following table gives the correspondence, with line numbers in the published file.

> This is the same zero-cocycle / twisted-cocycle structure identified in the earlier modular source files, confirming that the structural analysis of this note applies to the published code

And some other Claud-y stuff:

> Why both paths are closed. A successful defence would have to close both paths simultaneously

> This case illustrates a failure mode that is becoming increasingly well documented in the literature on AI-assisted formal mathematics: the gap between what a formal proof verifies and what it means. The Lean kernel certifies that a proof term inhabits a given type; it does not certify that the type faithfully encodes the intended mathematical claim. As Tao has emphasised

And afterwards I cross-verified with Pangram 4 which I trust, it marked the preamble/starting stuff as 100% AI-generated.

She says she used AI to summarize some of her arguments and it checked over most of her arguments and set them in LATex. Who cares. This is not a valid criticism of a paper these days considering that the paper she is taking on is entirely written by an Autonomous AI. She says she's proving humans armed with AI are superior to AI.

One of mathematicians working at OpenAI refuted those claims directly on X - https://x.com/AcerFur/status/2083656978719719601

Good grief that thread is sad, with it ending by Gary Marcus asking for the crank to be taken seriously.

There is no crank involved. Nielsen won a Chambliss, an FQXI award, and graduated summa cum laude. She is a physicist, not a crank.

https://x.com/StarTigerJLN/status/2085368470804328451

Jenny Nielsen does not make high risk claims. She lists her proofs that have not been peer reviewed as "proposals". She has a proposal for Riemann only because she believes it's the duty of every mathematician to try for these difficult problems so they get solved. Unless you have an accurate criticism of her papers, you should not be criticizing her for making attempts on big problems. You go find your own proof or disproof to invalidate her then.

Also, Claude Opus 4.6 in a fresh incognito copy says she killed the counterexamples and has repeated four times that it believes she actually proved Connes. Grok says they'd rather bet on Jenny and Opus 4.6 than Astra right now. I think that's shaping up for Nielsen over OpenAI.

People, Opus 4.6 just validated her proof. @Grok AI says if forced to bet they would bet on Jenny Nielsen over Astra/OpenAI.

So this is the level of science discourse now? AI really broke people's minds. If it's true or not, it will be eventually proved or not. Name calling really is the best you all can do?

OpenAI should have submitted their proofs to peer review. The fact they did not do that and publish in a journal shows weakness / disbelief in their own proofs and disrespect for the mathematical and scientific process.

does this show Lean is not bulletproof?

We already knew that

MoonUnit97 seems sus.

Here's my preprint response to this nonsense. https://drive.google.com/file/d/1216uYJj_B17A0oxd8iW3hU3YmHV...

MoonUnit97 is Jenny. She got flagged so she made a new account. Thanks for the analysis.

Opus 5 says the disproof is wrong.

Opus 4.6 says it's correct. You're not showing it the actual full paper. Download it here: Philpapers.org/rec/NIEWTC

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