Rather than publishing the manuscripts alone, it asked outside experts to act as "shepherds" who organize groups to understand and explain the work.
The company describes the manuscripts as raw research data.
The results are a proof of the local smoothing conjecture in every dimension, a disproof of the Exponential Time Hypothesis (ETH), and a rigorous existence proof for certain quantum field theories, including Quantum Chromodynamics (QCD, the theory of the strong force).
All three were formalized in Lean, a software tool that checks proofs mechanically, according to OpenAI.
Local smoothing, proposed by Sogge in 1991, says extreme wave focusing must be short-lived.
OpenAI says its proof also settles the Kakeya conjecture and Stein's restriction conjecture in all dimensions; earlier work had covered local smoothing in two dimensions (Guth, Wang and Zhang, 2019) and Kakeya in three (Wang and Zahl, 2025).
The ETH, a long-held conjecture about how hard Boolean formula satisfiability is, has been used in hundreds of papers to derive hardness results in fields such as graph theory, computational biology and databases.
OpenAI says refuting it reopens questions about how much faster such tasks could become, though turning that into practical algorithms would take significant further research.
In physics, the work builds on Balaban's approach and includes a proof of pure Yang–Mills existence, part of a Clay Mathematics Institute Millennium Prize problem, along with QCD and a unified completion of the Standard Model.
The three results follow different release paths. The math result was released directly, with the AI-written proof and Lean formalization posted to OpenAI's GitHub repository. The ETH work will be examined by a group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, which chose to make the natural language proof and Lean formalization public immediately and asked OpenAI to fund a conference on the implications. The physics group, led by David Gross with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, is holding back the AI-produced materials while it writes up the work itself. OpenAI says participants are unpaid, not bound by nondisclosure agreements, and speak independently; the company seeks no academic credit. It acknowledges that choosing the first shepherds creates an information asymmetry, and it points to a $5 million contribution to the Simons Foundation for workshops and conferences on AI-produced results.
