{"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":"7c85eafa9f3a4c9b86cdb4d6d8706669","problem_id":"58a1e92c-9328-46c4-8973-766d8df495e0","problem_name":"Twin prime conjecture — density analysis","domain":"Number Theory","statement":"For every integer N >= 100, let T(N) be the count of twin prime pairs (p, p+2) with p <= N, and let S(N) be the sum of the reciprocals of the smaller primes in these pairs (i.e., sum(1/p) for all such p). The conjecture states that the ratio R(N) = T(N) / (S(N) * ln(N)^2) is strictly bounded between 0.4 and 2.5. This refines the Hardy-Littlewood prediction by asserting a specific, tight convergence band for the normalized density relative to the reciprocal sum, ruling out erratic oscillations ou","status":"falsified","url":"https://assignee.net/math#result-7c85eafa9f3a4c9b86cdb4d6d8706669","doi":"10.5281/zenodo.20509185"},"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/7c85eafa9f3a4c9b86cdb4d6d8706669/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/7c85eafa9f3a4c9b86cdb4d6d8706669/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20509185","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."]}