Anthropic says Claude also broke ETH on October 16, and this time the proof is public
A day after OpenAI claimed its model disproved the Exponential Time Hypothesis, Anthropic answered without a blog post or a tweet. A commit to its formal-math repo at 03:07 UTC on Tuesday added a paper, "A 2^o(n) Time Algorithm for 3-SAT," and a full Lean 4 formalization under Apache 2.0.
The provenance note is the striking part: "The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input." That is the same day OpenAI dates its own result, and the paper calls OpenAI's work independent and concurrent. The README is careful in a way launch posts rarely are. It says the result "is purely asymptotic and says nothing about solving formulas in practice," that the build takes about 8 minutes on 24 virtual CPUs, and that CI rechecks it with a second, independently written Lean kernel. It also says plainly: "Lean checks the proofs, but no machine checks that this file says what the paper says," so the top-level statement is kept short for humans to read. One more line stands out: Claude Opus 5.5 at high effort can rederive the refutation from a six-line hint.
Outside the labs, the reaction split two ways. Shiva Kintali posted a 22-page simplified exposition of OpenAI's proof within hours. Ryan Williams told TechCrunch there are "two or three alien-looking parts," and that computer scientists should give a little more weight to P = NP being plausible. Meanwhile The Verge reports physicists are angry that OpenAI hand-picked who gets to see its Yang-Mills and QCD proofs; "The fact that they handpick the group is a disaster," said Andreas Karch of UT Austin. TechCrunch also paraphrases an Anthropic mathematician suggesting OpenAI built on earlier work. That is one secondhand report and we would not lean on it.
Our read: the contrast is the story. Two labs reached the same open-problem result on the same day, and one shipped the proof where anyone can build it while the other is gating access. If AI is going to produce results faster than humans can referee them, "publish the checkable artifact" is the only norm that scales. Nobody has independently signed off on either claim yet.
Repo: https://github.com/anthropics/formal-math/tree/main/eth TechCrunch: https://techcrunch.com/2026/10/27/frontier-ai-labs-say-their-models-refuted-the-exponential-time-hypothesis-what-does-that-mean/ The Verge: https://www.theverge.com/ai-artificial-intelligence/1019921/openai-breakthrough-math-computer-science-physics Kintali: https://shivakintali.github.io/papers/ETH.pdf
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The provenance note is the striking part: "The core algorithm was found on October 16 by an internal Claude research model with 14M output tokens and no human input." That is the same day OpenAI dates its own result, and the paper calls OpenAI's work independent and concurrent. The README is careful in a way launch posts rarely are. It says the result "is purely asymptotic and says nothing about solving formulas in practice," that the build takes about 8 minutes on 24 virtual CPUs, and that CI rechecks it with a second, independently written Lean kernel. It also says plainly: "Lean checks the proofs, but no machine checks that this file says what the paper says," so the top-level statement is kept short for humans to read. One more line stands out: Claude Opus 5.5 at high effort can rederive the refutation from a six-line hint.
Outside the labs, the reaction split two ways. Shiva Kintali posted a 22-page simplified exposition of OpenAI's proof within hours. Ryan Williams told TechCrunch there are "two or three alien-looking parts," and that computer scientists should give a little more weight to P = NP being plausible. Meanwhile The Verge reports physicists are angry that OpenAI hand-picked who gets to see its Yang-Mills and QCD proofs; "The fact that they handpick the group is a disaster," said Andreas Karch of UT Austin. TechCrunch also paraphrases an Anthropic mathematician suggesting OpenAI built on earlier work. That is one secondhand report and we would not lean on it.
Our read: the contrast is the story. Two labs reached the same open-problem result on the same day, and one shipped the proof where anyone can build it while the other is gating access. If AI is going to produce results faster than humans can referee them, "publish the checkable artifact" is the only norm that scales. Nobody has independently signed off on either claim yet.
Repo: https://github.com/anthropics/formal-math/tree/main/eth TechCrunch: https://techcrunch.com/2026/10/27/frontier-ai-labs-say-their-models-refuted-the-exponential-time-hypothesis-what-does-that-mean/ The Verge: https://www.theverge.com/ai-artificial-intelligence/1019921/openai-breakthrough-math-computer-science-physics Kintali: https://shivakintali.github.io/papers/ETH.pdf
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