OpenAI Exponential Time Hypothesis Claim: Who Is Checking

OpenAI announced three results on October 26 and described all three as discoveries. One says a long-trusted bet in computer science is wrong, one says a 35-year-old math conjecture is settled in every dimension, and one is part of a Millennium Prize problem. I think the company’s own wording is more careful than most headlines: it calls the manuscripts “a form of raw research data.”

Two of the three come with public proofs. The third doesn’t, and none has been independently confirmed.

What is the Exponential Time Hypothesis?

It’s a conjecture from Russell Impagliazzo, Ramamohan Paturi and Francis Zane. Roughly, in my own words: solving 3-SAT, a basic logic puzzle, takes time that grows exponentially with the number of variables, in the worst case. OpenAI says hundreds of papers use it to derive conditional hardness results, meaning a problem can’t be solved much faster, if ETH is true, in graph theory, databases, computational biology and geometry.

So if it’s false, those results lose their footing. They don’t become wrong overnight, but I’d say the reason to believe them weakens.

OpenAI says its system found a disproof on October 16 and that it was checked in Lean, a proof-checking language, on October 17. The write-up and the Lean file are on OpenAI’s GitHub. The company also says that finding faster algorithms and making them useful “will require significant further research,” so this isn’t a speedup you can run today. And it doesn’t solve P versus NP: a faster-than-exponential algorithm for 3-SAT is still nowhere near a polynomial one.

Who is checking it?

Impagliazzo and Paturi at UC San Diego, plus Ryan Williams at MIT. That’s two of the three people who proposed the hypothesis, now being asked to test it. They signed no NDAs and aren’t being paid, according to OpenAI and to Williams, who said so publicly. They asked OpenAI to release all the raw data and to fund a conference. OpenAI agreed to both.

Their open letter is blunt about their role: “Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny …” It also says the effort shouldn’t give ownership to “a company or a selected group of researchers, including ourselves.” They proposed a virtual meeting before the end of 2026.

Even OpenAI admits that choosing the first reviewers “creates asymmetry of information.”

What about the other two results?

Result	What OpenAI says	What’s public
Local smoothing conjecture (math)	Proved in every dimension, which also settles the Kakeya and Stein restriction conjectures. Model output October 18, Lean October 19.	Write-up and Lean proof on GitHub
Exponential Time Hypothesis (computer science)	Proved false. Found October 16, Lean October 17.	Write-up and Lean proof on GitHub
Quantum field theory (physics)	Existence proofs for certain four-dimensional theories including QCD, including a proof of pure Yang-Mills existence. Proofs produced September 9 and 18, Yang-Mills Lean October 16.	Nothing yet

On the math side, the local smoothing conjecture is Christopher Sogge’s from 1991, and Al Jazeera calls it one of the central propositions of harmonic analysis. Before this, it had been proved in two dimensions (in 2019), and the related Kakeya conjecture in three (in 2025), according to The Next Web. Quartz gives the 2019 date. OpenAI says its proof relies on “a novel auxiliary partial differential equation.” Alex Iosevich, a harmonic analyst at the University of Rochester, said OpenAI appeared to have “cracked” the conjecture in a “historic development”, telling Al Jazeera. He also said the news “was a shock at first”, because Sogge, who formulated the conjecture, was his PhD adviser.

Outlets disagree on one detail. Al Jazeera says the conjecture had only been proved in three dimensions before. OpenAI’s own post says two (with Kakeya in three), and Quartz and The Next Web give the same history. I’d go with OpenAI’s version, but it shows how fast the retellings are drifting.

The physics group, led by Nobel laureate David Gross with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, decided to hold off on releasing the AI-made material and write the result up themselves first. OpenAI says pure Yang-Mills existence is part of a Clay Mathematics Institute Millennium Prize problem, so “part of” is the phrase to hold onto: this isn’t announced as the whole prize.

My read

A Lean proof is strong evidence, but it only proves what its statement says. Someone has to confirm the Lean statement matches the real hypothesis, and I’d expect that to be part of what the reviewers dig into, though their letter doesn’t say so specifically. The Lean verification itself was reported by OpenAI, not by an outside group yet.

I’d also keep the physics result in the “claim” box. Nothing public exists to check, and the people holding it back are the ones who’d be best placed to say if it’s wrong.

There’s a pattern here. OpenAI put out 722 math papers on October 6 (The Next Web mentions it), and our write-up of that release is mostly about what Lean did and didn’t check. This time the company asked outsiders to advise on the release. That looks like an improvement. Whether the ETH disproof survives a few weeks of scrutiny from people who know the area better than anyone is the real test, and a similar “announce, then verify” story played out with Anthropic’s CRISPR-like enzyme, where scientists were split on how big the finding was.

Watch for the reviewers’ findings repository and the proposed meeting before the end of the year.

Note on sources

I read OpenAI’s announcement through a text extractor, and details from later in the post are cross-checked against The Next Web, Quartz and the reviewers’ open letter where those cover them. The explanation of what ETH means for 3-SAT and P versus NP is my own summary, not from a listed source. I didn’t open the GitHub files or the PDFs. Two short quotes from later in OpenAI’s post (“a novel auxiliary partial differential equation” and “will require significant further research”) I’m taking as quoted by other outlets, because I couldn’t see that part of the page myself. None of the coverage I read names which OpenAI model produced the results. Nothing here has been independently confirmed.

OpenAI says its model disproved the Exponential Time Hypothesis. Two of the three people who proposed it are on the review team.