{"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":"68b38389e7ec452c8216848ffc0f45b2","problem_id":"0b687d59-9114-42a0-bd3d-9fc0058b6e88","problem_name":"Catalan's conjecture (Mihailescu) — Lean4 formal proof","domain":"Number Theory","statement":"For any integer n > 1, if n is a perfect power (n = x^a with x > 1, a > 1), then the distance to the nearest other perfect power m (m != n, m = y^b with y > 1, b > 1) satisfies |n - m| > sqrt(n) * (ln(n))^0.8, with the sole exception of the pair (8, 9) where the distance is 1.","status":"falsified","url":"https://assignee.net/math#result-68b38389e7ec452c8216848ffc0f45b2","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/68b38389e7ec452c8216848ffc0f45b2/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/68b38389e7ec452c8216848ffc0f45b2/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."]}