{"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":"3f02ace5c31a489193dde51cdec3b42d","problem_id":"3f8b9926-f691-4998-b32e-434a876c83ae","problem_name":"Goldbach conjecture — computational extension","domain":"Number Theory","statement":"For every even integer n > 100, there exists a Goldbach partition n = p + q (with p <= q) such that the prime p lies within the interval [n/2 - sqrt(n), n/2]. Furthermore, the smallest such prime p satisfies the stronger bound: n/2 - p < sqrt(n) / ln(n).","status":"falsified","url":"https://assignee.net/math#result-3f02ace5c31a489193dde51cdec3b42d","doi":"10.5281/zenodo.20498996"},"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/3f02ace5c31a489193dde51cdec3b42d/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/3f02ace5c31a489193dde51cdec3b42d/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20498996","format":"text/html"}],"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."]}