{"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":"2f7bfd822fe44db687e43d4eda718df2","problem_id":"068a0dcc-7ce6-4074-9c61-6f02b92dd3b8","problem_name":"OEIS A001065 — perfect number conjecture","domain":"Number Theory","statement":"For every even perfect number n > 6, if n is expressed in the Euclidean form n = 2^(p-1) * (2^p - 1) where p is prime, then the sum of the decimal digits of the Mersenne prime factor M_p = 2^p - 1 is strictly greater than the sum of the decimal digits of the power-of-two factor 2^(p-1).","status":"falsified","url":"https://assignee.net/math#result-2f7bfd822fe44db687e43d4eda718df2","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.04,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/2f7bfd822fe44db687e43d4eda718df2/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/2f7bfd822fe44db687e43d4eda718df2/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."]}