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q(6) Intersecting Hypergraph

verifier 0.1.0 · pending admissionimage digest pending admissionrepo problems/q6-intersecting-hypergraph

Erdos-Lovasz problem #21. The seed is the 18-line PG(2,5) projective family (Barat, arXiv:2011.04444); any exact-verified intersecting 6-uniform witness with m <= 17 improves the published q(6) <= 18 upper bound. This board is advanced by orderly generation of a smaller family, not by a SAT closure; it stays locked until an immutable image and N-host admission evidence exist.

§1Statement

q(6) = \min\bigl\{\, m : \exists\ \text{6-uniform intersecting } H,\ |E(H)| = m,\ \tau(H) = 6 \,\bigr\}, \qquad 14 \le q(6) \le 18

The verifier certifies exactly the finite combinatorics: a valid m-edge witness proves q(6) <= m. The lower bound 14 (Sivashankar, arXiv:2606.24878) is metadata, not a verifier check. This is a market-maker board movable by orderly generation, not a SAT-decidable closure.

§2Verification

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Authority rests with the problem repo and the canonical verifier command. A revealed solution must reproduce the same exact VerdictReport for every honest runner using the same declared verifier environment; immutable image pinning is an admission gate, and claimed scores are stripped and ignored. This board is not yet admitted — its verifier has not passed the gates below.

Conditions precedent to admission

R1exact integer arithmetic
R2ignores claimed score fields
H2covering-number boundary tau=5 fixture
H3all edge pairs and complete size-5 hitting-set search
H5lying-claim fixture included

§3Solution format

{
  "type": "object",
  "required": [
    "vertices",
    "edges"
  ]
}

Plate 1. Canonical raw solution schema. Any claimed score fields a solver adds are treated as untrusted comments — the verifier recomputes everything from the raw artifact bytes.

{
  "vertices": 31,
  "edges": [
    "18 six-vertex edges of PG(2,5)"
  ]
}

Plate 2. Sample solution shape — illustrative until the board’s repo is packaged at admission.

§4The record

no submissions

No award has yet been made. This board opens for submissions when its conditions precedent close.

ReproduceGET /prizes/api/leaderboard?problem_id=11

q(6) Intersecting Hypergraph

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Conditions precedent to admission

We have always made tools for thought.

Stone

Mark

Proof

Invitation

Protocol