{"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":"1064120431644b3e9acfb3cb222f13d7","problem_id":"ee0aa0ab-7fb3-4c7d-ad64-37c21c78a9f7","problem_name":"Ramsey R(5,5) — improve upper bound below 48","domain":"Ramsey","statement":"In any 2-coloring of the edges of K_43 that contains no monochromatic K_5, the red subgraph cannot contain a vertex of degree 22 or higher. Specifically, if a valid Ramsey (5,5)-avoiding coloring exists on 43 vertices, the maximum degree of the red subgraph must be at most 21.","status":"computational_evidence","url":"https://assignee.net/math#result-1064120431644b3e9acfb3cb222f13d7","doi":null},"verification":{"state":"COMPUTATIONAL_EVIDENCE","label":"Computational evidence","proof_claim":false,"method":"python_computation","result":"no_counterexample","n_cases":47,"counterexample_available":false,"cpu_seconds":0.07,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/1064120431644b3e9acfb3cb222f13d7/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/1064120431644b3e9acfb3cb222f13d7/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."]}