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Search the graph by meaning. Each result carries its current verdict; open one to see its decomposition, provenance, and the reasoning behind the assessment.
ShowingImportancePrizesTopicGraph theory
The study of graphs — vertices, edges, connectivity, coloring, planarity, and extremal or random graph problems. Claims about graph-theoretic theorems, conjectures, and open problems belong here.
Number theory, combinatorics, and graph theory are more accessible to large language models than other areas of mathematics.
ContestedCredible evidence or argument exists on multiple sides.constitution →empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →Large language modelsNumber theoryCombinatoricsimportance · minorImportance 0.40, 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 →
Erdős's unit distance problem is equivalent to finding the maximum number of edges of a unit-distance graph on n vertices.
VerifiedThe claim traces to reliable primary sources through a clear chain of evidence.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Erdős unit distance conjectureDiscrete geometryimportance · settledImportance 0.10, 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 →
Every graph with n vertices and m ≥ 4n edges has crossing number Ω(m^3/n^2).
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 →Crossing lemmaimportance · settledImportance 0.15, 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 →
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If a claim here is wrong, or missing evidence, open it: every claim page carries its own entry for challenges, evidence, and corrections. If the graph is missing a claim entirely, propose it below. A proposal is reviewed on its merits; accepted claims are matched against the graph and enter it with their reasoning on record.