{"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":"39b2ddadc40c445784d990e374efc4b9","problem_id":"3f2b05a4-43ad-4e97-b417-8633a94d8f90","problem_name":"Van der Waerden w(2;4,4) — verify equals 35","domain":"Ramsey","statement":"w(2;4,4) = 35: every 2-coloring of {1,...,35} contains a monochromatic arithmetic progression of length 4. Verify computationally by showing all 2-colorings of {1,...,34} avoid monochromatic AP-4 (proving w > 34), and {1,...,35} does not.","status":"falsified","url":"https://assignee.net/math#result-39b2ddadc40c445784d990e374efc4b9","doi":"10.5281/zenodo.20440971"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.05,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/39b2ddadc40c445784d990e374efc4b9/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/39b2ddadc40c445784d990e374efc4b9/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20440971","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."]}