A paper deposited by Anthropic claims an internal Claude model also refuted the Exponential Time Hypothesis

A preprint on hexagonmath.org, listed as deposited by Anthropic on October 27, 2026, claims a deterministic algorithm for 3-SAT on n variables that runs in 2^o(n) time, which would refute the Exponential Time Hypothesis (ETH). It says the algorithm also solves the harder #3-SAT problem, which counts satisfying assignments, and that the result has been formalized in Lean 4.

According to the paper's provenance statement, an internal Claude research model found the core algorithm on October 16 using 14 million output tokens and no human input, and Anthropic researchers then worked with Claude to improve the presentation. The paper adds that an internal model at OpenAI claims, independently and concurrently, to have proven a similar result; it cites OpenAI's own preprint of October 26. All of this is the authors' claim and has not been independently verified.

The paper was shared on Hacker News (22 points, 6 comments by October 27), where one commenter noted that the claimed discovery date is the same as OpenAI's.