{"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":"e7d599128e7d45b98046739511b77230","problem_id":"ebb83cdc-3fec-4974-84a9-c5dccb942b46","problem_name":"Twin prime density — Hardy-Littlewood conjecture verification","domain":"Number Theory","statement":"For all integers x >= 100, the absolute difference between the actual count of twin prime pairs up to x and the Hardy-Littlewood prediction (2*C2*x/ln(x)^2) is strictly bounded by the square root of the prediction itself. That is, |pi_2(x) - Li_2(x)| < sqrt(Li_2(x)), where Li_2(x) approx 2*C2*x/ln(x)^2.","status":"falsified","url":"https://assignee.net/math#result-e7d599128e7d45b98046739511b77230","doi":null},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.05,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/e7d599128e7d45b98046739511b77230/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/e7d599128e7d45b98046739511b77230/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."]}