{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XGTPW4Z4DU5NG5TYSLMNSCZRK7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aec6f4fd7756d1228cad2d49f484c0cf32d858bd96e33677bc83965b225e1ae5","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-21T14:01:50Z","title_canon_sha256":"a88c05c979874dd58d96c2b383b9c2b5254fcceec23cc8226ecaa043e0a3ba10"},"schema_version":"1.0","source":{"id":"1402.5299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5299","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5299v2","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5299","created_at":"2026-05-18T01:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"XGTPW4Z4DU5N","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XGTPW4Z4DU5NG5TY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XGTPW4Z4","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:00fa7a79a9e2c04076ed95280789f515c548b10f85886ed5cc717ce3c64d7da6","target":"graph","created_at":"2026-05-18T01:44:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the previous works \\cite{N46,N47} authors have defined the oscillator-like system that associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev - Koornwinder oscillator. In this paper we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev - Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space $\\mathcal{H}$ of functions that are defined on a region which bounded by the Steiner hypocycloid. The functions are square-","authors_text":"E. V. Damaskinsky, V. V. Borzov","cross_cats":["math.CA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-21T14:01:50Z","title":"The algebra of two dimensional generalized Chebyshev - Koornwinder oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5299","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:27d816faf7a093836ede650144bdfb689177240e0037d12568803db409282e76","target":"record","created_at":"2026-05-18T01:44:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aec6f4fd7756d1228cad2d49f484c0cf32d858bd96e33677bc83965b225e1ae5","cross_cats_sorted":["math.CA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-02-21T14:01:50Z","title_canon_sha256":"a88c05c979874dd58d96c2b383b9c2b5254fcceec23cc8226ecaa043e0a3ba10"},"schema_version":"1.0","source":{"id":"1402.5299","kind":"arxiv","version":2}},"canonical_sha256":"b9a6fb733c1d3ad3767892d8d90b3157d8fe0e6218c43cde90b7deea259e8cc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9a6fb733c1d3ad3767892d8d90b3157d8fe0e6218c43cde90b7deea259e8cc4","first_computed_at":"2026-05-18T01:44:29.647218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:29.647218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B6/HxdnC9Z0qj2Li2ZzXsIm6/rjXDJ0NxiLC3Z9Oy6Mj1tGPAy3d+Z1JrbN31HoEnKzYp40ozCNgPu867Os0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:29.648004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27d816faf7a093836ede650144bdfb689177240e0037d12568803db409282e76","sha256:00fa7a79a9e2c04076ed95280789f515c548b10f85886ed5cc717ce3c64d7da6"],"state_sha256":"737ae71c1d56546538231c118318c05bc7def791a1327762cb47ec9121219632"}