OpenAI says its models proved Kakeya, refuted ETH, and tackled QCD existence

OpenAI says its models produced three results it is handing to academic shepherds: a proof of the local smoothing conjecture in every dimension, which it says also resolves the Kakeya and Stein restriction conjectures; a Lean-verified claim that the Exponential Time Hypothesis is false; and a constructive existence proof for certain four-dimensional gauge theories including QCD and pure Yang–Mills. For the maths result it is releasing the AI write-up and Lean proof publicly; for computer science, a group led by Impagliazzo, Paturi and Williams will explain the ETH claim while OpenAI publishes the natural-language and Lean artifacts on GitHub; for physics, a group led by David Gross will steward the work and has asked to hold AI artifacts while they write it up. OpenAI frames the manuscripts as raw research data pending community verification and says participation is voluntary, unpaid and independent.