{"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":"17b23802a7a14aa9b2ac654261e673cc","problem_id":"14ca72f2-1123-463b-9a13-2a9dd90feba9","problem_name":"Cap set problem — F_3^n maximum","domain":"Combinatorics","statement":"Conjecture: For n=6, the maximum size of a cap set in F_3^6 is exactly 112, and this maximum is uniquely achieved (up to affine equivalence) by the set of vectors with weight congruent to 1 modulo 3 in the specific coordinate subspace defined by the first 6 dimensions of the 7-dimensional maximal cap construction. Furthermore, any cap set in F_3^6 of size 112 must contain a subset of 28 vectors that form an affine plane of order 3 (isomorphic to F_3^2).","status":"falsified","url":"https://assignee.net/math#result-17b23802a7a14aa9b2ac654261e673cc","doi":"10.5281/zenodo.20502717"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.02,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/17b23802a7a14aa9b2ac654261e673cc/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/17b23802a7a14aa9b2ac654261e673cc/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20502717","format":"text/html"}],"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."]}