{"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":"3ab4d13b1159441097635a859fcd5f4f","problem_id":"068a0dcc-7ce6-4074-9c61-6f02b92dd3b8","problem_name":"OEIS A001065 — perfect number conjecture","domain":"Number Theory","statement":"For any even perfect number n > 6, let p be the largest prime factor of n (which is also the Mersenne prime exponent's base, i.e., n = 2^(p-1)*(2^p - 1)). The sum of the proper divisors of the Mersenne prime component (2^p - 1), which is exactly 1, plus the sum of the proper divisors of the power-of-two component (2^(p-1)), which is 2^(p-1) - 1, differs from the square root of n by less than 10% of the value of the Mersenne prime itself. Specifically, | (1 + (2^(p-1) - 1)) - sqrt(n) | < 0.1 * (2","status":"falsified","url":"https://assignee.net/math#result-3ab4d13b1159441097635a859fcd5f4f","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.05,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/3ab4d13b1159441097635a859fcd5f4f/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/3ab4d13b1159441097635a859fcd5f4f/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."]}