Two of the results went up on GitHub on Monday. The first, in mathematics, is a proof of local smoothing for the Euclidean wave equation in every spatial dimension of at least two, from which, OpenAI says, the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates follow throughout the conjectured range. OpenAI released this one as direct model output, as it did in its October 6 mass release, after its advisers recommended letting researchers work out the explanations themselves.
The second, in computer science, is the most dramatic: a paper presenting a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. If the proof holds, the 3-SAT case refutes the Exponential Time Hypothesis (ETH), a foundational assumption in complexity theory since 1999. An independent working group led by Russell Impagliazzo and Ramamohan Paturi, who formulated the original hypothesis, and MIT professor Ryan Williams will examine and explain the proof. At the group's request the materials, including a Lean-formalized proof, were made public immediately, together with an open letter to the community on norms for handling AI-generated breakthroughs.
The third result, in physics, has not been released in full: OpenAI describes it as a mathematically rigorous existence proof of certain interacting quantum field theories with gauge fields and fermions in four dimensions, including quantum chromodynamics (QCD) and a "unified completion of the Standard Model". Nobel laureate David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov to shepherd the work before publication.
The outside-shepherd model is a response to criticism of the October release, which left mathematicians with hundreds of unexplained documents. But it is contested too: the AGMAI panel of math advisers that OpenAI itself assembled recommended a day earlier that AI companies not adopt the practice of giving selected people early access, citing unequal access, "borrowed reputation" and biased selection, and proposed instead releasing output on scholarly repositories with Lean-formalized proofs and funding for the people checking the results. None of the three results has yet been peer reviewed.