{"data":{"id":"barnette-1969","statement_oneline":"Every cubic 3-connected planar bipartite graph is Hamiltonian.","statement_full_latex":"Every 3-connected cubic planar bipartite graph has a Hamiltonian cycle (Barnette).","source":{"title":"Barnette's conjecture (1969)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Barnette%27s_conjecture","year":1969,"area":"math.CO"},"renown":{"score":3,"rationale":"The surviving refinement after Tutte's related conjecture fell to counterexample in 1946 and Tait's to Tutte himself.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Finite witness with a Hamiltonicity oracle (exponential but feasible to ~90 vertices); exhaustively verified through 90 vertices, which is exactly why the open region is expensive.","subscores":{"finite_witness":5,"oracle_cost":2,"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-barnette-1969","conjecture_id":"barnette-1969","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/barnette-1969/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/barnette-1969/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}