OpenAI closed another Monday with three claimed breakthroughs — in computer science, mathematics and physics — plus a new and contested answer to the question of who gets to check them.
What was claimed
Computer science. A paper titled "The Exponential Time Hypothesis is False" gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. Applied to 3-SAT, that would refute the Exponential Time Hypothesis: the 1999 conjecture, from Russell Impagliazzo and Ramamohan Paturi, that 3-SAT cannot be solved in subexponential time. ETH is load-bearing for large parts of fine-grained complexity, where it supplies the hardness assumptions behind hundreds of conditional lower bounds. The write-up and a Lean formalisation went to GitHub today, at the verification group's request.
Mathematics. "Local smoothing for the Euclidean wave equation" uses an auxiliary partial differential equation to establish Sogge's local smoothing for waves in every spatial dimension of at least two. OpenAI says the result also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates across the interior of the conjectured range. The model output is being released as-is, the same way the company handled its October 6 drop.
Physics. OpenAI describes "a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions", including quantum chromodynamics and "a unified completion of the Standard Model of particle physics". That material has not been released in full.
Who checks it
For computer science, an independent group led by Impagliazzo, Paturi and MIT's Ryan Williams will examine and explain the proof. For physics, David Gross will lead a group that includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. For the mathematics result, OpenAI says its advisers recommended releasing the raw model output so researchers can work through their own explanations.
The company also posted an open letter asking how credit should recognise the work of checking, fixing and explaining AI results, what expectations should govern early access, and how students should be trained while methods shift.
The timing is awkward
The designations arrived one day after the Advisory Group on Mathematics and Artificial Intelligence, hosted at the Institute for Advanced Study, recommended that AI companies not adopt the practice of naming who receives results first — citing unequal access, borrowed reputation and biased selection. Its preferred route: post to scholarly repositories, ship Lean-formalised proofs, disclose how problems were chosen, and fund the people doing the understanding. OpenAI had already put $5 million toward that last item in mid-October.
The track record is mixed enough to matter. Of the 719 manuscripts OpenAI released on October 6, only about 42% carried a completed Lean formalisation, according to an analysis by LLM Odds; researchers at Cambridge and King's College found at least one case where the Lean code did not match the English proof it was meant to certify. Compiling code is not the same as a checked proof, and a checked proof is not yet an understood result.
Why it matters
If the ETH result survives scrutiny it does not add a theorem so much as remove a pillar: an entire industry of conditional lower bounds rests on 3-SAT being hard. If it does not survive, it becomes the sharpest test yet of whether "the model output is on GitHub" counts as publication.
Both outcomes are informative, which is why the next few weeks of expert commentary are the story. None of the three claims should be treated as established until the shepherding groups report; the computational-complexity materials are public precisely so that other people can try to break them.
