{"schema":"https://assignee.net/schemas/math-result-v1","schema_version":"1.0","contract_version":"math-result-v1.0","schema_documentation":"https://assignee.net/schemas","changelog_url":"https://assignee.net/changelog","publisher":{"name":"Assignee Research","url":"https://assignee.net"},"result":{"id":"948db96904504e718875e2c12e2233ec","problem_id":"e7987e25-6bf4-44b8-9382-cf876c90f4be","problem_name":"Zarankiewicz z(n,n;3,3) — improve upper bound","domain":"Combinatorics","statement":"For n≥3, the maximum number of ones in an n×n matrix avoiding a 3×3 all-ones submatrix is strictly less than n^2, and the difference n^2 - z(n,n;3,3) grows at least linearly with n.","status":"falsified","url":"https://assignee.net/math#result-948db96904504e718875e2c12e2233ec","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.03,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/948db96904504e718875e2c12e2233ec/manifest.json","format":"application/json"}],"interpretation":"Computational evidence is not a formal proof. Formal verification is claimed only when public Lean4 source is attached.","limitations":["Python check code, local file paths, and private execution logs are not exposed in public manifests.","Computational evidence reports bounded search only and can be invalidated by later counterexamples.","Formal proof verification requires public Lean4 source; otherwise the record remains a proof attempt or report."]}