Exponential Time Hypothesis disproof confirmed by...?: live odds and probabilities

Market rules and resolution

On October 26, 2026, OpenAI announced that its AI system "proved that the ETH is false, a result that was subsequently verified in Lean." (see: https://openai.com/index/building-scientific-understanding-with-academic-communities/) This market will resolve to "Yes" if a disproof of the Exponential Time Hypothesis is confirmed through at least one of the qualifying confirmation methods listed below by the specified date, 11:59 PM ET. Otherwise, this market will resolve to "No". The "Exponential Time Hypothesis" refers to the conjecture formulated by Russell Impagliazzo and Ramamohan Paturi that the 3-SAT problem cannot be solved in subexponential time. A "disproof" refers to any mathematical proof that the Exponential Time Hypothesis is false, including the proof presented in OpenAI's paper titled "The Exponential Time Hypothesis is False" (https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf) and any corrected, revised, or extended version of it, whether by OpenAI or by others. Confirmations that only establish a weaker result, such as a faster algorithm that does not refute the Exponential Time Hypothesis, or that only establish that OpenAI's Lean code compiles, will not qualify. The qualifying confirmation methods are: (i) Peer-reviewed publication: a paper presenting a disproof, whether authored by OpenAI or by other researchers, is published in, or accepted for publication by, a reputable peer-reviewed scientific journal or peer-reviewed conference (e.g., STOC, FOCS, SODA). Preprints and other publications that have not completed peer review will not qualify. (ii) Independent verification: the review group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, any of these three researchers, or another credible researcher or research group unaffiliated with OpenAI, publicly confirms that a disproof is correct. The confirmation must state without qualification that the disproof is correct or that the Exponential Time Hypothesis is false (e.g., that the proof has been checked and found to be correct), and must be published by the verifying researcher, group, or its members, including via a paper, preprint, website, blog, or official social media account; confirmations relayed only by OpenAI will not qualify. A confirmation may be based on a review of the written proof, the Lean formalization, or both; a confirma