{"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":"fc9fc487c02e46c8bda81b45b93af029","problem_id":"58a1e92c-9328-46c4-8973-766d8df495e0","problem_name":"Twin prime conjecture — density analysis","domain":"Number Theory","statement":"For any integer N >= 100, let T(N) be the count of twin prime pairs (p, p+2) with p <= N. Let S_3(N) be the count of such pairs where the smaller prime p satisfies p mod 3 == 1. The conjecture states that the deviation of S_3(N) from exactly half of T(N) is bounded by the square root of the total count: |S_3(N) - T(N)/2| < sqrt(T(N)). This asserts a 'square-root cancellation' in the distribution of twin primes across the two allowable residue classes modulo 3, analogous to probabilistic expectat","status":"falsified","url":"https://assignee.net/math#result-fc9fc487c02e46c8bda81b45b93af029","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/fc9fc487c02e46c8bda81b45b93af029/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/fc9fc487c02e46c8bda81b45b93af029/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."]}