Hours after OpenAI announced that its internal models had disproved the Exponential Time Hypothesis (ETH), Anthropic posted its own claimed refutation on Tuesday, October 27: a Claude-written paper and a Lean-checked proof of a sub-exponential algorithm for 3-SAT. Anthropic says an internal Claude model found the core algorithm on October 16 with no human input, working “independently and concurrently” with OpenAI.

ETH, proposed in 1999, holds that 3-SAT cannot be solved in sub-exponential time, and hundreds of hardness results in theoretical computer science rest on it. Neither lab's proof has been peer-reviewed, and Anthropic's own paper cautions that the result “says nothing about solving formulas in practice.” OpenAI's version is now with an outside group led by two of ETH's original authors, Russell Impagliazzo and Ramamohan Paturi, alongside MIT's Ryan Williams.

The near-simultaneous claims turn a single-lab announcement into a race: two frontier labs say their models independently broke the same foundational assumption in the same month. What happens next depends on the reviewers, not the press releases.