{"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":"13761122992e44b8ad52898e67018b16","problem_id":"14ca72f2-1123-463b-9a13-2a9dd90feba9","problem_name":"Cap set problem — F_3^n maximum","domain":"Combinatorics","statement":"For n=6, the maximum size of a cap set in F_3^n is exactly 112. Furthermore, every maximal cap set of this size contains a subset of 28 points that forms a disjoint union of 4 affine planes of dimension 2 (2-flats), where no three of these planes are collinear in the quotient space.","status":"falsified","url":"https://assignee.net/math#result-13761122992e44b8ad52898e67018b16","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/13761122992e44b8ad52898e67018b16/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/13761122992e44b8ad52898e67018b16/paper.pdf","format":"application/pdf"}],"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."]}