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ShowingImportancePrizesTopicOpenAI
OpenAI, the AI research lab, and the systems it builds (e.g., GPT models, agent swarms). Claims attributing a result, capability, or failure to an OpenAI system belong here; claims about other labs' systems do not.
An internal OpenAI Codex model independently rediscovered the 2026 Jacobian conjecture counterexample.
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Jacobian conjecture2026 Jacobian counterexample constructionAI mathematical discoveryimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI's Navier-Stokes singularity proof depended essentially on Córdoba and Martínez-Zoroa's layered-cascade strategy
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Navier-Stokes singularityAI discovery creditimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI's AI-generated disproof of the unit distance conjecture meets a top mathematics journal's acceptance standard
SupportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →AI mathematical discoveryAI-assisted Erdős problem solvingErdős unit distance conjectureimportance · minorImportance 0.35, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
The published OpenAI unit distance manuscript is a human-edited exposition of the model's raw output, with references and explanatory material added afterward
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · verifiableA factual claim that could be checked directly against observation or primary records.constitution →AI discovery creditErdős unit distance conjectureAI mathematical discoveryimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI's unit distance paper adequately cites closely related prior ideas in the literature
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →AI-assisted Erdős problem solvingErdős unit distance conjectureAI discovery creditimportance · minorImportance 0.25, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI's counterexample to the Erdős unit distance conjecture is mathematically correct
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Erdős unit distance conjectureAI mathematical discoveryDiscrete geometryimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI researchers first examined the model's unit distance proof only after an automated grading pipeline had rated it correct
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →AI mathematical discoveryAI-assisted Erdős problem solvingErdős unit distance conjectureimportance · settledImportance 0.20, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
OpenAI's Navier-Stokes singularity proof was produced by roughly 10,000 autonomous AI agents running for about 88 hours
UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →AI mathematical discoveryNavier-Stokes singularityimportance · minorImportance 0.30, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →
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