{"data":{"id":"berge-fulkerson-1971","statement_oneline":"Every bridgeless cubic graph has six perfect matchings covering each edge exactly twice.","statement_full_latex":"Every bridgeless cubic graph admits six perfect matchings such that every edge lies in exactly two of them.","source":{"title":"Berge-Fulkerson conjecture (1971)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Berge%E2%80%93Fulkerson_conjecture","year":1971,"area":"math.CO"},"renown":{"score":3,"rationale":"Classic matching-theory conjecture tightly linked to snarks and the CDC conjecture.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Finite witness (a snark), exactly checkable by matching enumeration; verified for all known small snarks, leaving no obvious seed frontier.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":1,"seedability":2},"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-berge-fulkerson-1971","conjecture_id":"berge-fulkerson-1971","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/berge-fulkerson-1971/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/berge-fulkerson-1971/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}