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Suppose that $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are two orthogonal polynomial sequences such that %their derivatives of orders $k$ and $m$ (respectively) satisfy the structure relation $$ \\pi_N(x)\\,P_{n+m}^{(m)}(x)= \\sum_{j=n-M}^{n+N}r_{n,j}Q_{j+k}^{(k)}(x)\\quad (n=0,1,\\ldots)\\,, $$ where $r_{n,j}$ are complex number independent of $x$. It is shown that under natural constraints, $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are semiclassical orthogonal polynomial sequences. Moreover, their correspo"},"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":"1906.07715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-18T17:57:54Z","cross_cats_sorted":[],"title_canon_sha256":"322653e79d5994900f15bf96351c432e9b76330c9174415335ada397a76d3632","abstract_canon_sha256":"4165a604983bbd2ac197bfb9fd5168078292862a5dcce342cee96ed3432cc4d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:59.508225Z","signature_b64":"WrO/wJppMEQrUKn1xGoHLtMa/pvuzdkEauArRw74/1qpv5v0bqO0LaEkCAHlvaL2tgRM6HiFo0laLvMLlny0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8ee7ec0dcb161ed8a0f3df051b1cc71f4bf50754fad1d14e8bf24a6e7ef3236","last_reissued_at":"2026-05-17T23:42:59.507802Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:59.507802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On another extension of coherent pairs of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. Mbouna, K. Castillo","submitted_at":"2019-06-18T17:57:54Z","abstract_excerpt":"Let $M$ and $N$ be fixed non-negative integer numbers and let $\\pi_N$ be a polynomial of degree $N$. Suppose that $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are two orthogonal polynomial sequences such that %their derivatives of orders $k$ and $m$ (respectively) satisfy the structure relation $$ \\pi_N(x)\\,P_{n+m}^{(m)}(x)= \\sum_{j=n-M}^{n+N}r_{n,j}Q_{j+k}^{(k)}(x)\\quad (n=0,1,\\ldots)\\,, $$ where $r_{n,j}$ are complex number independent of $x$. It is shown that under natural constraints, $(P_n)_{n\\geq0}$ and $(Q_n)_{n\\geq0}$ are semiclassical orthogonal polynomial sequences. Moreover, their correspo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07715","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":"1906.07715","created_at":"2026-05-17T23:42:59.507877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.07715v1","created_at":"2026-05-17T23:42:59.507877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07715","created_at":"2026-05-17T23:42:59.507877+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZDXH5QG4WFQ6","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZDXH5QG4WFQ63CQP","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZDXH5QG4","created_at":"2026-05-18T12:33:33.725879+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/ZDXH5QG4WFQ63CQPHXYFDMOMOH","json":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH.json","graph_json":"https://pith.science/api/pith-number/ZDXH5QG4WFQ63CQPHXYFDMOMOH/graph.json","events_json":"https://pith.science/api/pith-number/ZDXH5QG4WFQ63CQPHXYFDMOMOH/events.json","paper":"https://pith.science/paper/ZDXH5QG4"},"agent_actions":{"view_html":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH","download_json":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH.json","view_paper":"https://pith.science/paper/ZDXH5QG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.07715&json=true","fetch_graph":"https://pith.science/api/pith-number/ZDXH5QG4WFQ63CQPHXYFDMOMOH/graph.json","fetch_events":"https://pith.science/api/pith-number/ZDXH5QG4WFQ63CQPHXYFDMOMOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH/action/storage_attestation","attest_author":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH/action/author_attestation","sign_citation":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH/action/citation_signature","submit_replication":"https://pith.science/pith/ZDXH5QG4WFQ63CQPHXYFDMOMOH/action/replication_record"}},"created_at":"2026-05-17T23:42:59.507877+00:00","updated_at":"2026-05-17T23:42:59.507877+00:00"}