{"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":"aac0f88db762449e8c6e8eab8aecc69a","problem_id":"c22c22ff-6b3c-4d20-b7ca-33af7f727d93","problem_name":"Ramsey multiplicity K_4 — minimum number of monochromatic K_4","domain":"Graph Theory","statement":"In any 2-coloring of K_18, the minimum number of monochromatic K_4 is exactly 18, and this minimum is achieved only by colorings where the graph of one color forms a specific structured graph related to the Turán graph T(18,3).","status":"falsified","url":"https://assignee.net/math#result-aac0f88db762449e8c6e8eab8aecc69a","doi":"10.5281/zenodo.20470251"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":4.29,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/aac0f88db762449e8c6e8eab8aecc69a/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/aac0f88db762449e8c6e8eab8aecc69a/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20470251","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."]}