{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:IYCUTKLNNV7CB4VC3YJD62X7B3","short_pith_number":"pith:IYCUTKLN","schema_version":"1.0","canonical_sha256":"460549a96d6d7e20f2a2de123f6aff0edc70f78f4a7448c0813294da015f7aaa","source":{"kind":"arxiv","id":"1107.5898","version":1},"attestation_state":"computed","paper":{"title":"On the Properties of Special Functions on the linear-type lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J.L. Cardoso, R.Alvarez-Nodarse","submitted_at":"2011-07-29T08:52:06Z","abstract_excerpt":"We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to $q$-classical polynomials are given."},"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":"1107.5898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-29T08:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"29518f0fcff3de225f30ed4ef1f5f243b175f39e5439269ec7604a5265beeed0","abstract_canon_sha256":"d8178d145f1d0407c08ec0abe02c46ae6a09e9c4e757a52501efc2754893b4ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:11.687432Z","signature_b64":"Udvjo1E3LGWfArd9pjKa95tf71ZPzHO6H+YUzVS3pNQrGU1M7llMGGv513KdJEt0iDDKab3JIzBY2Dkl4KEgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"460549a96d6d7e20f2a2de123f6aff0edc70f78f4a7448c0813294da015f7aaa","last_reissued_at":"2026-05-18T03:00:11.686857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:11.686857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Properties of Special Functions on the linear-type lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J.L. Cardoso, R.Alvarez-Nodarse","submitted_at":"2011-07-29T08:52:06Z","abstract_excerpt":"We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a special kind of lattices: the linear type lattices. In particular, using the integral representation of the solutions we obtain several difference-recurrence relations for such functions. Finally, applications to $q$-classical polynomials are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5898","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":"1107.5898","created_at":"2026-05-18T03:00:11.686943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.5898v1","created_at":"2026-05-18T03:00:11.686943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5898","created_at":"2026-05-18T03:00:11.686943+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYCUTKLNNV7C","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYCUTKLNNV7CB4VC","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYCUTKLN","created_at":"2026-05-18T12:26:32.869790+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/IYCUTKLNNV7CB4VC3YJD62X7B3","json":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3.json","graph_json":"https://pith.science/api/pith-number/IYCUTKLNNV7CB4VC3YJD62X7B3/graph.json","events_json":"https://pith.science/api/pith-number/IYCUTKLNNV7CB4VC3YJD62X7B3/events.json","paper":"https://pith.science/paper/IYCUTKLN"},"agent_actions":{"view_html":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3","download_json":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3.json","view_paper":"https://pith.science/paper/IYCUTKLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.5898&json=true","fetch_graph":"https://pith.science/api/pith-number/IYCUTKLNNV7CB4VC3YJD62X7B3/graph.json","fetch_events":"https://pith.science/api/pith-number/IYCUTKLNNV7CB4VC3YJD62X7B3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3/action/storage_attestation","attest_author":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3/action/author_attestation","sign_citation":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3/action/citation_signature","submit_replication":"https://pith.science/pith/IYCUTKLNNV7CB4VC3YJD62X7B3/action/replication_record"}},"created_at":"2026-05-18T03:00:11.686943+00:00","updated_at":"2026-05-18T03:00:11.686943+00:00"}