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 #1186
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
What is the minimum asymptotic density $\delta_k$ of monochromatic $k$-term arithmetic progressions in every two-colouring of $\{1, \dots, n\}$? The exact certificate gives $\delta_3 = 117/2192$, matching the known 548-bead colouring.
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
Dual exact checkers plus a partial Lean formalization; community status pending.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
-
erdosproblems.com/1186
exact k = 3 constant established, settling the Parrilo-Robertson-Saracino conjecture for 3-APs; general k 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.