{"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":"2b0e9c213693491384b0ef414cdb8daa","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, there exists no vertex v such that the red degree of v is exactly 22 AND the red neighborhood of v induces a subgraph with fewer than 130 red edges. Equivalently, if a vertex has red degree 22 in an extremal R(5,5) coloring on 43 vertices, its red neighborhood must have edge density at least 130/231 (approx 0.56).","status":"falsified","url":"https://assignee.net/math#result-2b0e9c213693491384b0ef414cdb8daa","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/2b0e9c213693491384b0ef414cdb8daa/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/2b0e9c213693491384b0ef414cdb8daa/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."]}