{"data":{"id":"ryser-1967","statement_oneline":"In an r-partite r-uniform hypergraph, the vertex cover number is at most (r-1) times the matching number.","statement_full_latex":"For every $r$-partite $r$-uniform hypergraph $H$, $\\tau(H) \\le (r-1)\\,\\nu(H)$ (Ryser). Open for all $r \\ge 4$.","source":{"title":"Ryser's conjecture (c. 1967; r=3 is Aharoni's theorem)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Ryser%27s_conjecture","year":1967,"area":"math.CO"},"renown":{"score":3,"rationale":"Generalizes König's theorem; the r=3 case (Aharoni 2001) is celebrated, r>=4 fully open.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Finite witness with ILP oracles; extremal examples from truncated projective planes seed the tight boundary; intense modern attention has produced tightness results but no counterexample direction.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":2,"seedability":3},"scored_by":"founder"},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-25","ranking_score":6,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"resolution_type":null,"resolver":null,"resolution_date":null,"evidence_url":null,"evidence_note":null,"method_note":null,"effective_status":"open","claims":[],"status_events":[{"id":"seed-ryser-1967","conjecture_id":"ryser-1967","status":"open","date":"2026-07-25T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[{"name":"claim","method":"POST","href":"/c/ryser-1967/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/ryser-1967/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}