OpenAI frontier model (specific version not disclosed)
Model-assisted construction of a point configuration reported to have more than $n^{1.014}$ unit-distance pairs.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős's Planar Unit Distance Conjecture
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
Erdős conjectured an $n^{1+o(1)}$ upper bound on the number of unit-distance pairs among $n$ points in the plane. A construction with more than $n^{1.014}$ pairs disproves that conjectured asymptotic upper bound; the exact extremal unit-distance problem remains open.
This statement is indexed from an attributed source. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
VibeMathed reports human expert verification and an arXiv write-up; VibeMath preserves that label as a source assertion.
Correctness: supported · statement fidelity: unaudited · peer review: none
Timeline
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Remarks on the disproof of the unit distance conjecture
The asymptotic conjecture was disproved; this does not determine the exact unit-distance extremal function.
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- VibeMath has not independently verified the mathematical claim.
- AI-attempt independence and training-data exposure are unknown unless explicitly documented.