{"data":{"id":"one-third-two-thirds-1968","statement_oneline":"Every finite non-totally-ordered poset has two elements x,y where the fraction of linear extensions with x below y is between 1/3 and 2/3.","statement_full_latex":"Every finite partially ordered set that is not a chain contains elements $x, y$ such that the proportion of linear extensions with $x < y$ lies in $[\\tfrac13, \\tfrac23]$.","source":{"title":"1/3-2/3 conjecture (Kislitsyn 1968; Fredman; Linial)","arxiv":null,"url":"https://en.wikipedia.org/wiki/1/3%E2%80%932/3_conjecture","year":1968,"area":"math.CO"},"renown":{"score":3,"rationale":"A jewel of order theory with deep ties to sorting complexity.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Finite poset witness; linear-extension counting is #P-hard but exact at small sizes; the constant 8/31 examples (the known extremes) are natural seeds; small cases exhaustively verified.","subscores":{"finite_witness":5,"oracle_cost":3,"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-one-third-two-thirds-1968","conjecture_id":"one-third-two-thirds-1968","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/one-third-two-thirds-1968/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/one-third-two-thirds-1968/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}