frontiers / frontier
e1271/1271 · statement.attested · reviewer:will-blair · 2026-06-10 · null→null
Reviewable change
back to reviewErdős Problem #564 remains OPEN. Statement: Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$-uniform hypergraph on $m$ vertices are $2$-coloured then there is a monochromatic copy of the complete $3$-uniform hypergraph on $n$ vertices. Is there some constant $c>0$ such that $$ R_3(n) \geq 2^{2^{cn}}? $$ Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.
A proposal; no authority until an accepted review event.
accept gate
0 of 4 on recordtimeline
vpr_8c5f8f6b9e93547bSEMANTIC-EDGE DRAFT -> Erdos #562 (vf_187280ca6f4d09c4) [specializes, confidence 0.9]: 564 is the r=3 special case of 562's general r-uniform hypergraph Ramsey number R_r(n), asking for monochromatic cliques in 2-colourings of complete 3-uniform hypergraphs. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.proposed
reason
SEMANTIC-EDGE DRAFT -> Erdos #562 (vf_187280ca6f4d09c4) [specializes, confidence 0.9]: 564 is the r=3 special case of 562's general r-uniform hypergraph Ramsey number R_r(n), asking for monochromatic cliques in 2-colourings of complete 3-uniform hypergraphs. -- LLM-drafted (20-agent extraction, 2026-06); NOT adjudicated. Accept or reject via `vela proposals accept/reject` under reviewer authority.
provenance
proposed by
agent:semantic-edge-extractor
actor type
human
created at
2026-06-10
target type
finding
affected
inspect finding →Erdős Problem #564 remains OPEN. Statement: Let $R_3(n)$ be the minimal $m$ such that if the edges of the $3$-uniform hypergraph on $m$ vertices are $2$-coloured then there is a monochromatic copy of the complete $3$-uniform hypergraph on $n$ vertices. Is there some constant $c>0$ such that $$ R_3(n) \geq 2^{2^{cn}}? $$ Topics: graph theory, ramsey theory, hypergraphs. Erdős prize: $500. Statement is machine-verified in Lean (formal-conjectures). OEIS: possible.
vf_8fdce4bf9419e970Read-only frontier; diff not recomputed.
Erdős problems frontier receives a reviewable source, finding, caveat, replication, evaluation, or proof-affecting edit.
The packet names affected record objects, evidence, rationale, reviewer-facing fields, and expected proof impact.
Schema, provenance, benchmark, contradiction, and proof checks decide whether the request is ready to read.
A steward accepts, rejects, caveats, revises, or retracts the request under an inspectable identity.
Only the accepted event mutates frontier state. Atlases, constellations, and search update from that record state.
Jump to a section, signal, campaign, document, primitive, work path, frontier, record index, atlas, constellation, agent, capability, or full-state search.