{"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":"6168a219a5854c3f88060f07f8b58e44","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 integers encountered in the Collatz trajectory of n before reaching 1. Define the 'Odd-Step Parity Signature' P(n) as the sum of the indices (0-based) of all odd elements in S(n) that are congruent to 3 modulo 4. The conjecture states that for all n in the range [2, 10^6], P(n) is never a perfect square greater than 1.","status":"falsified","url":"https://assignee.net/math#result-6168a219a5854c3f88060f07f8b58e44","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/6168a219a5854c3f88060f07f8b58e44/manifest.json","format":"application/json"},{"type":"report","label":"Public report PDF","url":"https://assignee.net/math/6168a219a5854c3f88060f07f8b58e44/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."]}