{"data":{"id":"reconstruction-1942","statement_oneline":"Every graph on at least 3 vertices is determined up to isomorphism by its multiset of vertex-deleted subgraphs.","statement_full_latex":"Any two graphs on $n \\ge 3$ vertices with the same deck of vertex-deleted subgraphs are isomorphic (Kelly-Ulam).","source":{"title":"Reconstruction conjecture (Kelly 1942, Ulam)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Reconstruction_conjecture","year":1942,"area":"math.CO"},"renown":{"score":4,"rationale":"A foundational mystery of graph theory, open for 80+ years.","scored_by":"founder"},"attackability":{"score":1,"rationale":"A counterexample is a finite pair of graphs, and exhaustive search has cleared all graphs through 13 vertices (McKay) -- the remaining space is brutally large and unstructured.","subscores":{"finite_witness":5,"oracle_cost":2,"freshness":1,"seedability":1},"scored_by":"founder"},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-25","ranking_score":4,"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-reconstruction-1942","conjecture_id":"reconstruction-1942","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/reconstruction-1942/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/reconstruction-1942/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}