{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1997:WNQY7OOXM33O25NT635E4KC2TT","short_pith_number":"pith:WNQY7OOX","schema_version":"1.0","canonical_sha256":"b3618fb9d766f6ed75b3f6fa4e285a9ce661464de64c796749a4ce9a4fb7cc25","source":{"kind":"arxiv","id":"q-alg/9705006","version":1},"attestation_state":"computed","paper":{"title":"Separation of variables and integral relations for special functions","license":"","headline":"","cross_cats":["math.CA","math.QA"],"primary_cat":"q-alg","authors_text":"Evgueni K. Sklyanin, Vadim B. Kuznetsov","submitted_at":"1997-05-08T11:22:30Z","abstract_excerpt":"We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral relations for the continuous q-ultraspherical polynomials. The separating integral operator M expressed in terms of the Askey-Wilson operator is studied in detail: apart from writing down the characteristic (``separation'') equations it satisfies, we find its spectrum, eigenfunctions, inversion, invariants (invariant q-difference operators), and give its interpreta"},"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":"q-alg/9705006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1997-05-08T11:22:30Z","cross_cats_sorted":["math.CA","math.QA"],"title_canon_sha256":"08064df2e42d73bc8a2c3cddadcc491bae1cdd2a46a2cdfe8a96d144e607b816","abstract_canon_sha256":"3fbcd0b8294e1519a6c53502ce36330ffd17fe4242e465062f0327b4c2e37807"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:05.975515Z","signature_b64":"NPfJRfWDMlK9N3BcT8z857x9ajtYHmzhJTohqqF9oyfhd19lixDXSSZnO+qqtmJYRwAzah5UbSLjtnI5L6jIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3618fb9d766f6ed75b3f6fa4e285a9ce661464de64c796749a4ce9a4fb7cc25","last_reissued_at":"2026-05-18T01:27:05.975014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:05.975014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separation of variables and integral relations for special functions","license":"","headline":"","cross_cats":["math.CA","math.QA"],"primary_cat":"q-alg","authors_text":"Evgueni K. Sklyanin, Vadim B. Kuznetsov","submitted_at":"1997-05-08T11:22:30Z","abstract_excerpt":"We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral relations for the continuous q-ultraspherical polynomials. The separating integral operator M expressed in terms of the Askey-Wilson operator is studied in detail: apart from writing down the characteristic (``separation'') equations it satisfies, we find its spectrum, eigenfunctions, inversion, invariants (invariant q-difference operators), and give its interpreta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9705006","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9705006","created_at":"2026-05-18T01:27:05.975093+00:00"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9705006v1","created_at":"2026-05-18T01:27:05.975093+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9705006","created_at":"2026-05-18T01:27:05.975093+00:00"},{"alias_kind":"pith_short_12","alias_value":"WNQY7OOXM33O","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_16","alias_value":"WNQY7OOXM33O25NT","created_at":"2026-05-18T12:25:48.327863+00:00"},{"alias_kind":"pith_short_8","alias_value":"WNQY7OOX","created_at":"2026-05-18T12:25:48.327863+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT","json":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT.json","graph_json":"https://pith.science/api/pith-number/WNQY7OOXM33O25NT635E4KC2TT/graph.json","events_json":"https://pith.science/api/pith-number/WNQY7OOXM33O25NT635E4KC2TT/events.json","paper":"https://pith.science/paper/WNQY7OOX"},"agent_actions":{"view_html":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT","download_json":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT.json","view_paper":"https://pith.science/paper/WNQY7OOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=q-alg/9705006&json=true","fetch_graph":"https://pith.science/api/pith-number/WNQY7OOXM33O25NT635E4KC2TT/graph.json","fetch_events":"https://pith.science/api/pith-number/WNQY7OOXM33O25NT635E4KC2TT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT/action/storage_attestation","attest_author":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT/action/author_attestation","sign_citation":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT/action/citation_signature","submit_replication":"https://pith.science/pith/WNQY7OOXM33O25NT635E4KC2TT/action/replication_record"}},"created_at":"2026-05-18T01:27:05.975093+00:00","updated_at":"2026-05-18T01:27:05.975093+00:00"}