{"paper":{"title":"The 2D Smorodinsky--Winternitz II system and the Laguerre--Heun algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexei Zhedanov, Luc Vinet, Vutha Vichea Chea","submitted_at":"2026-05-30T21:57:22Z","abstract_excerpt":"We identify the quadratic symmetry algebra of the two-dimensional Smorodinsky--Winternitz II system with a Laguerre-type confluent Heun algebra. The system is separable in Cartesian and parabolic coordinates. The complementary Cartesian separation operator \\[\n  Y=\\partial_y^2-\\omega^2y^2+\\frac{1/4-c^2}{y^2} \\] is of Laguerre type, while the parabolic integral \\(W=L_2\\) is its algebraic Heun partner. With \\(Z=[Y,W]\\), the defining relations are \\[\n  [Y,Z]=16\\omega^2W-2bY,\\qquad\n  [W,Z]=6Y^2-4HY+2bW+8\\omega^2(1-c^2), \\] where \\(H\\) is central. This gives a direct superintegrable realization of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00903","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}