ETH Refutation Timeline

OpenAI and Anthropic each say an internal model refuted the Exponential Time Hypothesis (ETH), a long-standing conjecture in complexity theory, on the same day, Oct 16. OpenAI announced its result in a blog post on Oct 26; Anthropic published a paper on Hexagon and in its GitHub repository on Oct 27, committed at 03:07 UTC, about six hours after OpenAI's own repository update.

Found on the same day

OpenAI says “Our AI found its natural language disproof for the ETH on October 16th, 2026,” and that it formalized the result in Lean the next day. Anthropic's paper says its core algorithm “was found on October 16 by an internal Claude research model with 14M output tokens and no human input,” and that Anthropic researchers then worked with Claude on the presentation. OpenAI's paper is dated Oct 17 and revised Oct 25, the paper shows; Anthropic's is dated Oct 26, its own shows.

Two releases, hours apart

OpenAI's post names a group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT to verify the work, and says OpenAI agreed to the group's requests to make all raw data public and to fund a conference. Williams wrote on X that the group “signed no NDAs” and asked for the raw data, and that OpenAI “agreed to both.” Anthropic's paper is credited to Claude, and notes that “independently and concurrently, an internal model at OpenAI claims to have proven a similar result.”

What each Lean proof covers

Both papers state the same bound in n for counting satisfying assignments, 2^O(n log log n/√log n). OpenAI's Lean proof checks a weaker one, n(log log n)²/√log n in the exponent, and its scope note says “the October 25 manuscript gives the sharper time bound.” Anthropic's Lean statement carries the full bound on a Turing-style machine, and says the step to ordinary algorithms is made of “standard facts; they are not part of the Lean statements or proofs.” Its paper says no person is known to have checked its Lean proof.

Credit

OpenAI says it does not seek academic credit for the discoveries of its internal models. Levent Alpöge, one of Anthropic's own mathematicians, wrote on X on Oct 27 that he claims “absolutely zero credit for anything around this.” Neither lab claims a practical speedup: Anthropic's result “is purely asymptotic and says nothing about solving formulas in practice,” its repository says. The result is one of three OpenAI announced on Oct 26.