{"data":{"id":"harary-hill-k13","statement_oneline":"The crossing number of the complete graph K13 equals the Harary-Hill formula value 225.","statement_full_latex":"$\\mathrm{cr}(K_{13}) = 225$, the Harary-Hill value $\\tfrac14 \\lfloor \\tfrac{n}{2} \\rfloor \\lfloor \\tfrac{n-1}{2} \\rfloor \\lfloor \\tfrac{n-2}{2} \\rfloor \\lfloor \\tfrac{n-3}{2} \\rfloor$ at $n = 13$; the conjecture is proved only through $n = 12$.","source":{"title":"Harary-Hill conjecture, smallest open case","arxiv":null,"url":"https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)","year":1958,"area":"math.CO"},"renown":{"score":3,"rationale":"The concrete frontier of a 65-year-old drawing conjecture.","scored_by":"founder"},"attackability":{"score":2,"rationale":"A refutation is a single drawing of K13 with fewer than 225 crossings -- a finite, instantly checkable witness; decades of SAT-assisted and heuristic drawing searches have matched, never beaten, the bound.","subscores":{"finite_witness":5,"oracle_cost":5,"freshness":1,"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-harary-hill-k13","conjecture_id":"harary-hill-k13","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/harary-hill-k13/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/harary-hill-k13/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}