{"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":"e1ea6af8e40f4d3ab81106c6b56370a5","problem_id":"d5ffd6bf-5994-481d-8c61-4cc9c5f7767a","problem_name":"Collatz conjecture — structural pattern search","domain":"Number Theory","statement":"For any integer n > 1, let S(n) be the set of odd numbers encountered in the Collatz trajectory of n before reaching 1. Let m = min(S(n)). Then the total stopping time (number of steps to reach 1) is strictly less than m^2 + m.","status":"falsified","url":"https://assignee.net/math#result-e1ea6af8e40f4d3ab81106c6b56370a5","doi":"10.5281/zenodo.20563120"},"verification":{"state":"FALSIFIED","label":"Falsified","proof_claim":false,"method":"python_computation","result":"falsified","n_cases":0,"counterexample_available":true,"cpu_seconds":0.02,"lean4_source_public":false},"artifact_set":[{"type":"manifest","label":"Math result manifest","url":"https://assignee.net/math/e1ea6af8e40f4d3ab81106c6b56370a5/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/e1ea6af8e40f4d3ab81106c6b56370a5/paper.pdf","format":"application/pdf"},{"type":"external_record","label":"DOI","url":"https://doi.org/10.5281/zenodo.20563120","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."]}