{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:BGEYQHCD7KE4CMXVRS4QJGYGA7","short_pith_number":"pith:BGEYQHCD","schema_version":"1.0","canonical_sha256":"0989881c43fa89c132f58cb9049b0607caf3e0585c18a0eb1271152bd603e71a","source":{"kind":"arxiv","id":"math/0702388","version":2},"attestation_state":"computed","paper":{"title":"Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Barry Simon (Caltech), David Damanik (Rice), Rowan Killip (UCLA)","submitted_at":"2007-02-13T19:07:18Z","abstract_excerpt":"We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations."},"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":"math/0702388","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2007-02-13T19:07:18Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9e52f74dc5475a48d17e129d1f81f45aea62481db72085ac0540511be14ecca0","abstract_canon_sha256":"5514451e3eb6672922a8f6db196e6f8c45d42997d5d1e9be1d2341c535339acb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:23.103971Z","signature_b64":"9cFo6uyUfAj+SxABp2Cylhf+3PdsjGKabo9tdXyX1McyyXJ+5pBgSvsvNwT8OOCPYAnKL9PQHkDn8QVEzuuRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0989881c43fa89c132f58cb9049b0607caf3e0585c18a0eb1271152bd603e71a","last_reissued_at":"2026-05-18T02:30:23.103558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:23.103558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbations of Orthogonal Polynomials With Periodic Recursion Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Barry Simon (Caltech), David Damanik (Rice), Rowan Killip (UCLA)","submitted_at":"2007-02-13T19:07:18Z","abstract_excerpt":"We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702388","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":""},"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":"math/0702388","created_at":"2026-05-18T02:30:23.103630+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0702388v2","created_at":"2026-05-18T02:30:23.103630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702388","created_at":"2026-05-18T02:30:23.103630+00:00"},{"alias_kind":"pith_short_12","alias_value":"BGEYQHCD7KE4","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"BGEYQHCD7KE4CMXV","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"BGEYQHCD","created_at":"2026-05-18T12:25:55.427421+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/BGEYQHCD7KE4CMXVRS4QJGYGA7","json":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7.json","graph_json":"https://pith.science/api/pith-number/BGEYQHCD7KE4CMXVRS4QJGYGA7/graph.json","events_json":"https://pith.science/api/pith-number/BGEYQHCD7KE4CMXVRS4QJGYGA7/events.json","paper":"https://pith.science/paper/BGEYQHCD"},"agent_actions":{"view_html":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7","download_json":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7.json","view_paper":"https://pith.science/paper/BGEYQHCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0702388&json=true","fetch_graph":"https://pith.science/api/pith-number/BGEYQHCD7KE4CMXVRS4QJGYGA7/graph.json","fetch_events":"https://pith.science/api/pith-number/BGEYQHCD7KE4CMXVRS4QJGYGA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7/action/storage_attestation","attest_author":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7/action/author_attestation","sign_citation":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7/action/citation_signature","submit_replication":"https://pith.science/pith/BGEYQHCD7KE4CMXVRS4QJGYGA7/action/replication_record"}},"created_at":"2026-05-18T02:30:23.103630+00:00","updated_at":"2026-05-18T02:30:23.103630+00:00"}