{"data":{"id":"kill-polya-1958","statement_oneline":"Pólya's conjecture (1919): at least half the integers up to any bound have an odd number of prime factors.","renown":{"score":3,"rationale":"Classic 1919 conjecture on prime factor parity.","scored_by":"founder"},"attackability":{"score":3,"rationale":"Finite integer witness (near 9x10^8) with a computable but nontrivial oracle; famous for surviving massive numerical evidence.","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":1,"seedability":2},"scored_by":"founder"},"ranking_score":9,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"status":"confirmed","added":"1958-01-01","resolution_type":"counterexample","resolver":"C. B. Haselgrove (existence), R. S. Lehman (explicit: n = 906,180,359)","resolution_date":"1958-01-01","evidence_url":"https://doi.org/10.1112/s0025579300001480","evidence_note":"Disproved nonconstructively in 1958; smallest explicit counterexample found 1960/1980. Verified for decades before failing.","method_note":"The canonical warning that numerical evidence to 10^8 proves nothing.","effective_status":"confirmed","claims":[],"status_events":[{"id":"seed-kill-polya-1958","conjecture_id":"kill-polya-1958","status":"confirmed","date":"1958-01-01T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}