{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2000:HIGDH4UQZ4I4IMGIQYBLI722FD","short_pith_number":"pith:HIGDH4UQ","schema_version":"1.0","canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","source":{"kind":"arxiv","id":"nlin/0010048","version":2},"attestation_state":"computed","paper":{"title":"Darboux transforms on Band Matrices, Weights and associated Polynomials","license":"","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Mark Adler, Pierre van Moerbeke","submitted_at":"2000-10-27T14:34:50Z","abstract_excerpt":"Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In \"Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems\", Comm. Math. Phys.\n  207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to \"moments\", polynomials defined by determinants of matrices involving these moments and $2m+1$-step relations between them, thus leading to $2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect does it have on the $m$-periodic sequence of weights and on the associated polynomials ? T"},"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":"nlin/0010048","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2000-10-27T14:34:50Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"88a5268651076c20237cc1a3434249182496d09f2387ed4f54ad33dc5f6cfd54","abstract_canon_sha256":"bebfeab5dabbf0858e379888987a4a2f85ee62c2eff95de23d42ddf1a8c0b3ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:41:36.818470Z","signature_b64":"UeaO0dKuHGcMlDw1F6NP6n1Zk6VLbKbMWMe+jg18N2bjoP+zMLf4gDK51WBY7ZhhuOJFCui+f36v+uu7tnHLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0c33f290cf11c430c88602b47f5a28deae5ba98c5ca7a5f756615f6721907a","last_reissued_at":"2026-07-04T14:41:36.818090Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:41:36.818090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Darboux transforms on Band Matrices, Weights and associated Polynomials","license":"","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Mark Adler, Pierre van Moerbeke","submitted_at":"2000-10-27T14:34:50Z","abstract_excerpt":"Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In \"Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems\", Comm. Math. Phys.\n  207, pp. 589-620 (1999), we have shown that $m$-periodic sequences of weights lead to \"moments\", polynomials defined by determinants of matrices involving these moments and $2m+1$-step relations between them, thus leading to $2m+1$-band matrices $L$. Given a Darboux transformations on $L$, which effect does it have on the $m$-periodic sequence of weights and on the associated polynomials ? T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0010048","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/nlin/0010048/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"nlin/0010048","created_at":"2026-07-04T14:41:36.818150+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0010048v2","created_at":"2026-07-04T14:41:36.818150+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0010048","created_at":"2026-07-04T14:41:36.818150+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIGDH4UQZ4I4","created_at":"2026-07-04T14:41:36.818150+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIGDH4UQZ4I4IMGI","created_at":"2026-07-04T14:41:36.818150+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIGDH4UQ","created_at":"2026-07-04T14:41:36.818150+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.05294","citing_title":"Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity","ref_index":38,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD","json":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD.json","graph_json":"https://pith.science/api/pith-number/HIGDH4UQZ4I4IMGIQYBLI722FD/graph.json","events_json":"https://pith.science/api/pith-number/HIGDH4UQZ4I4IMGIQYBLI722FD/events.json","paper":"https://pith.science/paper/HIGDH4UQ"},"agent_actions":{"view_html":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD","download_json":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD.json","view_paper":"https://pith.science/paper/HIGDH4UQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0010048&json=true","fetch_graph":"https://pith.science/api/pith-number/HIGDH4UQZ4I4IMGIQYBLI722FD/graph.json","fetch_events":"https://pith.science/api/pith-number/HIGDH4UQZ4I4IMGIQYBLI722FD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/action/storage_attestation","attest_author":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/action/author_attestation","sign_citation":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/action/citation_signature","submit_replication":"https://pith.science/pith/HIGDH4UQZ4I4IMGIQYBLI722FD/action/replication_record"}},"created_at":"2026-07-04T14:41:36.818150+00:00","updated_at":"2026-07-04T14:41:36.818150+00:00"}