trailAn AI system has autonomously produced research mathematics of a quality publishable in a leading journal
The 2026 AI mathematical results mark a phase transition in AI models' research mathematics capability.
OpenAI's AI-generated disproof of the unit distance conjecture meets a top mathematics journal's acceptance standard
OpenAI's counterexample to the Erdős unit distance conjecture is mathematically correct
Erdős's unit distance problem was one of the most important long-standing open problems in discrete geometry
bedrock · value premise
OpenAI's unit distance paper adequately cites closely related prior ideas in the literature
bedrock · value premise
The published OpenAI unit distance manuscript is a human-edited exposition of the model's raw output, with references and explanatory material added afterward
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claim · evaluativeA judgment of worth or quality against some standard: good, fair, effective.constitution →claim page ↗︎
An AI system has autonomously produced research mathematics of a quality publishable in a leading journal
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 →
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this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →↑supportedEvidence favors the claim, but the chain is incomplete or the sources are secondary.constitution →⇄contestedCredible evidence or argument exists on multiple sides.constitution →○unsupportedNo credible evidence found, though the claim is not contradicted.constitution →✕contradictedAvailable evidence weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌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 →verified factopen questionvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →Fig. Detail falls off with distance; every claim is an address.