{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WYEUPPZT7WK4WGSQEBTNMUA7ZQ","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":"908dcb2299565e70afe2dc433ca1154c8b5501caf78c36db80356571ad8ad402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-10T13:55:27Z","title_canon_sha256":"5584cb4381b0d3066b74db9419ddc96193f7a2935ffd9ea9969452f0cc268225"},"schema_version":"1.0","source":{"id":"1101.1817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1817","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1817v1","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1817","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"WYEUPPZT7WK4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WYEUPPZT7WK4WGSQ","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WYEUPPZT","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:7130689f5269a4a37ad590e9512ecaa4a8148737352944d78c972bd12b464765","target":"graph","created_at":"2026-05-18T02:22:59Z","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":"We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-\\beta. We combine both lattices to obtain the bi-lattice N \\cup (N+1-\\beta) and show that the orthogonal polynomials on this bi-lattice have recurrence coefficients which satisfy a non-linear system of recurrence equations, which we can identify as a limiting case of an (asymmetric) discrete Painlev\\'e equation.","authors_text":"Christophe Smet, Walter Van Assche","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-10T13:55:27Z","title":"Orthogonal polynomials on a bi-lattice"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1817","kind":"arxiv","version":1},"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:ba7e60be7bb3422dcb3a3c3d512a143886d5148e760c4bcc5953656df5e24e77","target":"record","created_at":"2026-05-18T02:22:59Z","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":"908dcb2299565e70afe2dc433ca1154c8b5501caf78c36db80356571ad8ad402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-01-10T13:55:27Z","title_canon_sha256":"5584cb4381b0d3066b74db9419ddc96193f7a2935ffd9ea9969452f0cc268225"},"schema_version":"1.0","source":{"id":"1101.1817","kind":"arxiv","version":1}},"canonical_sha256":"b60947bf33fd95cb1a502066d6501fcc134aeb09b65bc075e02db76a42586493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b60947bf33fd95cb1a502066d6501fcc134aeb09b65bc075e02db76a42586493","first_computed_at":"2026-05-18T02:22:59.368925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:59.368925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ugp2VrVQ43tcVs8xuquvt+UDHRc1rdnZ7BwX0+NPb0vaMRTpwdFUa3oO93cmbNaqL1WaytoyUTDf2R3giYwTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:59.369444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba7e60be7bb3422dcb3a3c3d512a143886d5148e760c4bcc5953656df5e24e77","sha256:7130689f5269a4a37ad590e9512ecaa4a8148737352944d78c972bd12b464765"],"state_sha256":"71fd17bdcfcd22de60baa056ea00144b23484accb0804f36e0190e23819669f9"}