{"id":11,"slug":"q6-intersecting-hypergraph","repoId":"q6-intersecting-hypergraph","title":"q(6) Intersecting Hypergraph","status":"locked","mode":"construction","direction":"minimize","scoreName":"edge count","seedBest":"18/1","currentBest":"18/1","optimum":"14/1","minImprovement":"1/1","bountyEth":"0.00","challengeWindowHours":72,"postingBondEth":"0.00","challengeBondEth":"0.00","verifierVersion":"0.1.0","verifierImage":"sha256:local-dev","verifierCommand":"make verify SOLUTION=path","repoPath":"problems/q6-intersecting-hypergraph","tagline":"A market-maker board on the q(6) upper bound: move it by orderly generation of a smaller intersecting family.","description":"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.","verifierStandard":["R1 exact integer arithmetic","R2 ignores claimed score fields","H2 covering-number boundary tau=5 fixture","H3 all edge pairs and complete size-5 hitting-set search","H5 lying-claim fixture included"],"solutionSchema":{"type":"object","required":["vertices","edges"]},"sampleSolution":{"vertices":31,"edges":["18 six-vertex edges of PG(2,5)"]},"statement":"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","statementCaveat":"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.","source":"local-phase-0","pool":null,"funding":null,"chainProvenance":{"settlementState":"local-only","reconciliationOk":false,"source":"static-portal-data","note":"Phase 0 portal state only: no deployed registry manifest or indexer reconciliation is attached to this problem yet.","fundingTargetDeployed":false}}