TL;DR: OpenAI says an internal AI system found a faster theoretical algorithm for a fundamental logic problem. Outside researchers are organizing a public examination; their participation is not a certification of the result.

Satisfiability asks whether a set of true-or-false choices can satisfy a collection of constraints. The Exponential Time Hypothesis says that a central version of this problem cannot be solved in subexponential time in the number of variables.

OpenAI’s October 26 release claims to refute that hypothesis and publishes a manuscript and Lean formalization. This would not, by itself, settle P versus NP or establish a practical speedup for today’s software.

Russell Impagliazzo, Ramamohan Paturi and Ryan Williams explain why checking and understanding the claim is its own substantial piece of work:
docs.google.com/document/d/1adB0IhJgLzsmbfCgoLrtoJTjnlPf74UnyjMo35P5JHo/edit

Public manuscript and proof files:
github.com/openai/math/tree/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026

I have inspected the release and the researchers’ letter, not independently checked the proof.