{"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":"63dbbefc6b334b33b1251ed421d7956a","problem_id":"58a1e92c-9328-46c4-8973-766d8df495e0","problem_name":"Twin prime conjecture — density analysis","domain":"Number Theory","statement":"For every integer N >= 10,000, let T(N) be the count of twin prime pairs (p, p+2) with p <= N. Let S_odd(N) be the sum of the smaller primes p in these pairs where p ends in the digit 3 or 9, and S_even(N) be the sum where p ends in 1 or 7. The conjecture states that the absolute difference |S_odd(N) - S_even(N)| is strictly bounded by 0.15 * N * T(N) / ln(N). This refines the expected equidistribution of twin prime residues modulo 10 by proposing a specific decay rate for the cumulative bias.","status":"falsified","url":"https://assignee.net/math#result-63dbbefc6b334b33b1251ed421d7956a","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/63dbbefc6b334b33b1251ed421d7956a/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/63dbbefc6b334b33b1251ed421d7956a/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."]}