OddsDesk

Rules

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 confirmation based on the Lean formalization will qualify if it states that the formalized result establishes that the Exponential Time Hypothesis is false. Statements that the review is ongoing, that no errors have been found so far, or that the disproof appears likely to be correct will not qualify. Confirmations published or made public after the specified date will not be considered, even if the underlying review took place before it. OpenAI's employees, contractors, and investors are considered affiliated with OpenAI. The review group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, and its members, will not be considered affiliated with OpenAI. The review group's statement that its involvement should not be taken as certification of the claim will not prevent a subsequent qualifying confirmation by the group or its members from counting toward resolution. Statements, social media posts, or press releases by OpenAI or its affiliates, media reports that only relay such claims, and the Lean formalization published by OpenAI will not alone qualify. The resolution source for this market will be a consensus of credible sources and relevant scientific experts verifying the legitimacy of the qualifying confirmation.