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The Burr-Erdős hypercube Ramsey conjecture

Theorem 1.1: there is an absolute constant $C$ with $R(Q_n)\le C2^n$ for every $n\ge0$ ; with the two-block lower bound $3\cdot2^{n-1}-1$ this determines the order of $R(Q_n)$ . Consequences: linear Ramsey bounds for subgraphs occupying a fixed fraction of a cube, such as Cartesian powers of paths and other subgraphs of $Q_d$ . Not shown: any numerical value of $C$ , whether $R(Q_n)/2^n$ converges, or the general Burr-Erdős question for other dense families.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Burr-Erdős hypercube Ramsey conjecture · Hypercube Ramsey conjecture · Problem 181

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed record: The Burr-Erdős hypercube Ramsey conjecture

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No independent mathematician has checked this yet. Checked here: abstract, introduction and Theorem 1.1 of the TeX source, read against Burr and Erdős's cube question as the manuscript cites it and against erdosproblems.com Problem 181, which states it as $R(Q_n)\ll2^n$ and listed it as open when fetched on 7 October 2026. The statement matches. The proof is long (eighteen sections of regime analysis, patch tilings and resampling dynamics) and was not refereed. No Lean formalization; the README cautions that unformalized results could have issues.