{"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":"b77b197f38ef42b48057de9d0b5c2d00","problem_id":"adc211dd-5961-4dd5-bd3d-d0e458e1020f","problem_name":"Ramsey R(4,6) — computational bounds","domain":"Ramsey","statement":"In any 2-coloring of the edges of K_35 that avoids a red K_4 and a blue K_6 (if such a coloring exists), the maximum degree of any vertex in the red subgraph must be strictly less than 12. That is, Δ(Red) ≤ 11.","status":"falsified","url":"https://assignee.net/math#result-b77b197f38ef42b48057de9d0b5c2d00","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.08,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/b77b197f38ef42b48057de9d0b5c2d00/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."]}