OpenAI says an internal model disproved the Exponential Time Hypothesis, a conjecture hundreds of computer-science papers rely on, and asks the conjecture's authors to review it

OpenAI said on Monday 26 October that one of its internal, unnamed models produced a disproof of the Exponential Time Hypothesis (ETH), a conjecture about how hard the Boolean satisfiability problem is to solve, The Next Web and Engadget both report. OpenAI's own post refused our reader twice, so the details here are the two outlets'.

Both outlets report two more claimed results: a proof of the local smoothing conjecture in every dimension, and a proof that certain interacting quantum field theories exist in four dimensions. The Next Web reports that the ETH disproof was found on 16 October, checked in the Lean proof assistant the next day, and published on GitHub.

The review is led by Russell Impagliazzo and Ramamohan Paturi of the University of California, San Diego, who first proposed the hypothesis, and Ryan Williams of MIT, The Next Web reports. In an open letter quoted by The Next Web, they write: “Our involvement should not be taken as certification of the claim.” Engadget reports that OpenAI will not seek academic credit for the results.

This is a separate claim from the quasi-Riemann proof that the Switchboard reported on 17 and 26 October. If the disproof holds, the many results that assume ETH would lose that footing.

• Reported OpenAI says an internal model produced a disproof of the Exponential Time Hypothesis, checked in Lean, The Next Web reports; Engadget reports the same claim. The Next Web
• Reported OpenAI also claims the local smoothing conjecture and a four-dimensional quantum field theory result, and will not seek academic credit, Engadget reports. Engadget
• Reported The reviewers say their involvement is not a certification of the claim, in an open letter quoted by The Next Web. The Next Web