{"data":{"id":"singmaster-1971","statement_oneline":"Some absolute constant bounds how many times any number greater than 1 appears in Pascal's triangle.","statement_full_latex":"There is a constant $C$ such that every integer $> 1$ appears at most $C$ times as a binomial coefficient (Singmaster). No number is known to appear more than 8 times (3003 appears 8 times).","source":{"title":"Singmaster's conjecture (1971)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Singmaster%27s_conjecture","year":1971,"area":"math.NT"},"renown":{"score":3,"rationale":"Charismatic number-theory conjecture; interior-solution finiteness proved for the central strip by Matomäki-Radziwill-Shao-Tao-Teräväinen (2021).","scored_by":"founder"},"attackability":{"score":2,"rationale":"A 'counterexample' means finding numbers with ever more representations -- a finite, verifiable witness per candidate; searches beyond 10^60 have found nothing past 8, but the search itself is cheap to extend.","subscores":{"finite_witness":5,"oracle_cost":4,"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-singmaster-1971","conjecture_id":"singmaster-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/singmaster-1971/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/singmaster-1971/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}