{"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":"1f3a254de256402895a75dcf3ad2d328","problem_id":"0d5894f9-bdfb-45f4-8b32-c02f166d1046","problem_name":"Goldbach conjecture — extend computational verification","domain":"Number Theory","statement":"For every even integer n >= 12, there exists a Goldbach partition n = p + q (with p <= q) such that the smaller prime p satisfies p < sqrt(n) * ln(n) AND p is a quadratic residue modulo the smallest prime factor of n/2. If n/2 is prime, p must be a quadratic residue modulo 3.","status":"falsified","url":"https://assignee.net/math#result-1f3a254de256402895a75dcf3ad2d328","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/1f3a254de256402895a75dcf3ad2d328/manifest.json","format":"application/json"}],"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."]}