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Erdős Problem #183: Multicolor Triangle Ramsey

Let $R(3;k)$ be the least $n$ such that every $k$-colouring of the edges of $K_n$ contains a monochromatic triangle. Determine $\lim_{k\to\infty} R(3;k)^{1/k}$ (a \$250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 1, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Erdős Problem #183: Multicolor Triangle Ramsey · Erdős #183 · Problem 183

Confidence: Not scored

Registry verification: lean verified · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Astra (internal preview)
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Erdős Problem #183: Multicolor Triangle Ramsey

specialist registry · passed

Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.

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Lean certificate (MulticolorTriangleRamsey.lean)

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

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Quantum Parallel Repetition

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Manuscripts (ten-proofs paper, PDF)

paper · pending

paper link supplied by the VibeMathed registry.