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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.00903","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-30T21:57:22Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ca3c92efd6fcec4448fca706484e9233d8cb97f7027cf19575730a3ba63d948b","abstract_canon_sha256":"7a8257c0bb243893627811ee24e869967c8d1f0972cc813c25b94bb585bd84bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:09.187333Z","signature_b64":"gkP5aenntpY/RNuj0mFOk9uRGKL3TufawS+Az5gW7hYnNTuCfB84Y6lDvYk17yqpELCzu0WlybNH9bwcyOZrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bc6923500d2398412922d8dc31c5f5b04ea8c14f929ee96a08bc5f7cc135d04","last_reissued_at":"2026-06-02T01:04:09.186898Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:09.186898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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