{"data":{"id":"hadamard-668-1893","statement_oneline":"Does a Hadamard matrix of order 668 exist? (Smallest unresolved order of the Hadamard conjecture.)","statement_full_latex":"The Hadamard conjecture asserts a $\\pm 1$ matrix $H$ of order $4k$ with $HH^{T} = 4k\\,I$ exists for every $k$. The smallest order for which existence is unknown is $668$.","source":{"title":"Hadamard conjecture (Hadamard 1893; Paley 1933); smallest open order 668","arxiv":null,"url":"https://en.wikipedia.org/wiki/Hadamard_matrix","year":1893,"area":"math.CO"},"renown":{"score":4,"rationale":"A 130-year-old conjecture with the rare property of a concrete smallest open instance.","scored_by":"founder"},"attackability":{"score":3,"rationale":"The witness is a single explicit 668x668 sign matrix, instantly verifiable; the search space is astronomically large and decades of algebraic constructions have missed 668, but SAT/algebraic hybrid search is a live and legitimate route.","subscores":{"finite_witness":5,"oracle_cost":5,"freshness":2,"seedability":3},"scored_by":"founder"},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-25","ranking_score":12,"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-hadamard-668-1893","conjecture_id":"hadamard-668-1893","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/hadamard-668-1893/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/hadamard-668-1893/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}