GPT-5.6 Star Fleet (Claude Fable 5 referee)
The source does not provide a sufficiently specific role description.
Provider: OpenAI / Anthropic · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Erdős Problem #130
VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise statement
For an infinite planar set in strong general position, how large can the chromatic and clique numbers of its positive-integer-distance graph be - in particular, can the chromatic number be infinite? Yes: there is such a set, no three collinear and no four concyclic, with infinite chromatic number.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Lean-checked end to end; community review pending.
Correctness: supported · statement fidelity: audited · peer review: none
Timeline
-
erdosproblems.com/130
the infinite-chromatic subquestion is proved; the rest of the problem remains open
Known method families
argument (source-reported)
Source-reported tools: argument.
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.
- VibeMath has not independently audited the mathematical statement, proof, or novelty claim.