{"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":"2d0ba4abd21f436696d6b7449774d0ac","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 contains no red K_4 and no blue K_6, the red subgraph cannot contain a vertex of degree exactly 8. Specifically, the set of red degrees in such an extremal coloring must exclude the integer 8.","status":"falsified","url":"https://assignee.net/math#result-2d0ba4abd21f436696d6b7449774d0ac","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/2d0ba4abd21f436696d6b7449774d0ac/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/2d0ba4abd21f436696d6b7449774d0ac/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."]}