OpenAI claims three new scientific results — this time with academic shepherds

On October 26, OpenAI announced three results produced by its internal model: a proof of Sogge’s local smoothing conjecture in every dimension, which settles the Kakeya conjecture across the board; a refutation of the Exponential Time Hypothesis (ETH), a workhorse assumption of computational hardness; and existence proofs for interacting quantum field theories including QCD. Unlike the October 6 dump of 722 manuscripts, this release ran through external “shepherds” — three working groups that each chose how, and whether, to publish. Awkward timing: one day earlier, AGMAI — the independent math advisory group OpenAI had convened — recommended that AI companies not designate privileged recipients at all.

Key points

• Three results, three dates: local smoothing model output Oct 18, Lean formalization Oct 19; ETH natural-language proof Oct 16, Lean Oct 17; Yang–Mills existence Sept 9, QCD Sept 18, Yang–Mills Lean Oct 16.
• Three release strategies: math — raw model output published directly; CS — everything public immediately with the group explaining it; physics — AI artifacts withheld while the group writes its own paper.
• The shepherds: the CS group is led by ETH’s original proposers Russell Impagliazzo and Ramamohan Paturi (UC San Diego) with MIT’s Ryan Williams; the physics group by 2004 physics Nobel laureate David Gross.
• The objection came first: per The Verge, the AGMAI advisory panel said on Oct 25 that AI companies should not adopt designated privileged recipients.
• Continuity: 3 of the 722 manuscripts released Oct 6 were withdrawn on Oct 7, per the repository’s history file.

How the shepherd mechanism works

Per OpenAI’s blog post, it asked outside experts to organize groups to understand the new results, then let each group set the release terms. Four principles are stated explicitly: transparency about the collaboration’s existence, with no NDAs; OpenAI seeks no academic credit for its models’ discoveries; the working group gets credit for its writeups; participation is voluntary and unpaid. The three groups parted ways immediately. The math group kept the October 6 playbook and published raw model output. The CS group made everything public at once, invited the community to help organize an open examination of the ETH claim, and got OpenAI to fund a conference on the implications. The physics group held its AI-produced artifacts back and will write the paper itself. OpenAI concedes the tradeoff: picking shepherds means picking who gets involved first, and the information asymmetry is real.

The three results are not equally solid

The math result is the only one with full public material: a natural-language paper plus a Lean formalization, machine-checked as of October 19, in the openai/math repository. Sogge posed the local smoothing conjecture in 1991, and progress had come one dimension at a time — Hong Wang and Joshua Zahl proved the three-dimensional Kakeya conjecture in 2025, and per The Verge Wang won the Fields Medal in July 2026 for that work. The model’s proof uses a novel auxiliary partial differential equation to cover every spatial dimension of at least two, and implies Stein’s spherical restriction estimates along the way. The ETH refutation is also Lean-formalized: the formalization doc proves a deterministic algorithm exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space; the 3-SAT case kills ETH, the assumption behind hundreds of hardness papers. The physics claim is the heaviest and the least visible. The natural-language proofs (Yang–Mills on Sept 9, QCD on Sept 18) and a Yang–Mills existence Lean formalization completed Oct 16 all remain unreleased (as of Oct 27 neither is findable in the openai/math repository). “A unified completion of the Standard Model” is OpenAI’s own framing — IT Home’s read is narrower, that a sub-problem on the path to the Millennium prize is claimed solved. Until the working group’s review is done, it is a claim, not a result.

What others say: cheers, doubts, timing

The announcement drew hundreds of comments across two Hacker News threads within a day (the announcement thread passed 700 points, the ETH paper thread 500, checked Oct 27 via the Algolia API). Complexity-theory readers called the ETH refutation seismic while damping the hype: several comments stress that subexponential is not polynomial, so the update on P versus NP is modest. On physics, practitioners were cooler — one notes an existence proof only makes the mass-gap question well-posed, far from proving the gap; another points out QCD has 45 years of experimental success, so “it exists” was never the doubt. The timing drew the most attention: per The Verge, the AGMAI panel declared on Oct 25 — one day before the announcement — that AI companies should avoid designated privileged recipients, citing unequal access, borrowed reputation and biased selection, and instead recommended scholarly repositories, Lean formalizations and funding for understanding the results. OpenAI’s next-day announcement did nearly all of that, except that a shepherd list is itself a designated list.

Our take: process is the story

Next to last month’s 722 manuscripts, the real novelty is process. That release saw three withdrawals and fourteen repairs the next day, along with a “stop” letter from its advisory group; this one recruited field leaders before announcing, formalized in Lean first, and sat on the physics result rather than overclaim it in public. The shepherd mechanism is one answer to the question AlphaProof Nexus publishing in Science left open — how AI results clear peer review: put the reviewers on stage before the audience arrives. For mathematicians and computer scientists, the material is directly usable; the Lean files are on GitHub. For everyone else, watch two things: when the physics group’s paper lands, and whether the $5 million OpenAI is contributing through the Simons Foundation turns “digesting AI output” into paid work. As for whether the four principles are PR — the test comes the next time OpenAI holds a headline result and the shepherds say no.

What to watch

The CS group’s open examination and the promised conference have no dates yet. The physics group’s paper, and the withheld AI artifacts behind it, are the first real test of the mechanism. The open letter’s three questions — expectations for early access, how credit should be split, and how to support students — are collecting responses through a Google Docs link carried in The Verge’s report.