{"data":{"id":"lonely-runner-1967","statement_oneline":"Among k runners on a unit circle with distinct constant speeds, each runner is at some time at distance at least 1/k from all others.","statement_full_latex":"For $k$ runners with pairwise distinct speeds on $\\mathbb{R}/\\mathbb{Z}$ starting at $0$, every runner is at some time at circular distance $\\ge 1/k$ from all the others (Wills 1967, Cusick). Open for $k \\ge 8$.","source":{"title":"Lonely runner conjecture","arxiv":null,"url":"https://en.wikipedia.org/wiki/Lonely_runner_conjecture","year":1967,"area":"math.NT"},"renown":{"score":3,"rationale":"Beloved Diophantine-approximation problem; settled only through 7 runners.","scored_by":"founder"},"attackability":{"score":2,"rationale":"Reduces to integer speed vectors, so a counterexample for fixed k is finitely searchable in principle; k=8 is the frontier, with tight known configurations as seeds; view-obstruction structure makes violations unlikely.","subscores":{"finite_witness":4,"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-lonely-runner-1967","conjecture_id":"lonely-runner-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/lonely-runner-1967/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lonely-runner-1967/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}