{"data":{"id":"jacobian-n2-1939","statement_oneline":"The Jacobian conjecture in dimension 2: every polynomial map of the complex plane with nonzero constant Jacobian determinant is invertible.","statement_full_latex":"Every polynomial map $F:\\mathbb{C}^2 \\to \\mathbb{C}^2$ with $\\det JF$ a nonzero constant has a polynomial inverse. (The general conjecture, posed by Keller in 1939, was refuted in July 2026 for all $n \\ge 3$; the original two-variable case remains open.)","source":{"title":"Keller (1939); surviving case after the July 2026 refutation of JC(n) for n >= 3","arxiv":null,"url":"https://en.wikipedia.org/wiki/Jacobian_conjecture","year":1939,"area":"math.AG"},"renown":{"score":5,"rationale":"The surviving case of the conjecture whose refutation ignited the July 2026 AI counterexample wave; overnight the most-watched open problem in algebraic geometry.","scored_by":"founder"},"attackability":{"score":2,"rationale":"A counterexample would be an explicit pair of polynomials, machine-verifiable exactly; but n=2 has genuinely different structure (known to hold up to degree 100 by Moh), so the n=3 mechanism does not transfer. Expect a stampede regardless.","subscores":{"finite_witness":5,"oracle_cost":4,"freshness":4,"seedability":2},"scored_by":"founder"},"status":"open","last_verified_open":"2026-07-25","added":"2026-07-25","ranking_score":10,"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-jacobian-n2-1939","conjecture_id":"jacobian-n2-1939","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/jacobian-n2-1939/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/jacobian-n2-1939/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}