{"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":"ad6e319a126640d59bb94fd97ac551ca","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 there exists no other perfect power m = y^b (with y > 1, b > 1) in the interval (n, n + n^(2/3)], except for the specific case where n = 8 (2^3) and m = 9 (3^2). This conjecture asserts that the gap between consecutive perfect powers grows strictly faster than n^(2/3) for all n > 8, refining the known lower bounds on perfect power gaps.","status":"falsified","url":"https://assignee.net/math#result-ad6e319a126640d59bb94fd97ac551ca","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/ad6e319a126640d59bb94fd97ac551ca/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/ad6e319a126640d59bb94fd97ac551ca/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."]}