{"paper":{"title":"Quantum Painlev\\'e Equations: from Continuous to Discrete","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CA","nlin.SI"],"primary_cat":"math.QA","authors_text":"Alfred Ramani, Basil Grammaticos, Hajime Nagoya","submitted_at":"2008-06-09T14:13:50Z","abstract_excerpt":"We examine quantum extensions of the continuous Painlev\\'e equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlev\\'e equations II, IV and V. From their auto-B\\\"acklund transformations we derive the contiguity relations which we interpret as the quantum analogues of the discrete Painlev\\'e equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.1466","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}