{"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":"bb34d8f54e2641fb81afddc2809cbd1c","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 the edges of K_18 that achieves the global minimum number of monochromatic K_4 subgraphs, the resulting color classes (graphs) must be isomorphic to each other. Furthermore, each color class must have an automorphism group of order at least 18.","status":"falsified","url":"https://assignee.net/math#result-bb34d8f54e2641fb81afddc2809cbd1c","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.06,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/bb34d8f54e2641fb81afddc2809cbd1c/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/bb34d8f54e2641fb81afddc2809cbd1c/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."]}