{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MH2K5CPCJX5CLHM4O3X5DJ3RBY","short_pith_number":"pith:MH2K5CPC","schema_version":"1.0","canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","source":{"kind":"arxiv","id":"2606.04640","version":1},"attestation_state":"computed","paper":{"title":"From local to global asymptotic behaviour of orthogonal polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Artur Nicolau, Roman Bessonov","submitted_at":"2026-06-03T09:09:52Z","abstract_excerpt":"Let $\\{\\phi^*_n\\}$ be the sequence of reflected orthogonal polynomials on the unit circle $\\partial \\mathbb{D}$ generated by a measure $\\mu$ of Szeg\\H{o} class, and let $D_{\\mu}$ be the Szeg\\H{o} function of $\\mu$. We prove the uniform Ces\\`aro asymptotics $$ \\sup_{z \\in \\Gamma_\\zeta}\\Biggl(\\frac{1}{n}\\sum_{k = 0}^{n-1}\\Bigl||\\phi_k^*(z) D_{\\mu}(z)|^2 - 1\\Bigr|\\Biggr) \\to 0, \\qquad n \\to \\infty, $$ for almost all Stolz angles $\\Gamma_{\\zeta}$, $\\zeta\\in \\partial \\mathbb{D}$. This extends a well-known asymptotic result of M\\'at\\'e, Nevai, and Totik (1991) from the local scale $O(1/n)$ near $\\pa"},"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":"2606.04640","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-06-03T09:09:52Z","cross_cats_sorted":[],"title_canon_sha256":"5d2900d68bd74c280c33117b8d2f18fd8e796369a17fe209a96186036ff1c0a6","abstract_canon_sha256":"443650ce3b2350ed957a17d812ece23fe1def406c911e8e6019ae4e2ca2ad581"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:22.652094Z","signature_b64":"4Yku+IPnVy1ApPmyB1ufxVKNV7QWTb4xhD9WsdO4xhlNaRTGP8m9fuYGAPzzi6JoxVOVJb0Pb+ndcW4OGwSeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","last_reissued_at":"2026-06-04T01:09:22.650579Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:22.650579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From local to global asymptotic behaviour of orthogonal polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Artur Nicolau, Roman Bessonov","submitted_at":"2026-06-03T09:09:52Z","abstract_excerpt":"Let $\\{\\phi^*_n\\}$ be the sequence of reflected orthogonal polynomials on the unit circle $\\partial \\mathbb{D}$ generated by a measure $\\mu$ of Szeg\\H{o} class, and let $D_{\\mu}$ be the Szeg\\H{o} function of $\\mu$. We prove the uniform Ces\\`aro asymptotics $$ \\sup_{z \\in \\Gamma_\\zeta}\\Biggl(\\frac{1}{n}\\sum_{k = 0}^{n-1}\\Bigl||\\phi_k^*(z) D_{\\mu}(z)|^2 - 1\\Bigr|\\Biggr) \\to 0, \\qquad n \\to \\infty, $$ for almost all Stolz angles $\\Gamma_{\\zeta}$, $\\zeta\\in \\partial \\mathbb{D}$. This extends a well-known asymptotic result of M\\'at\\'e, Nevai, and Totik (1991) from the local scale $O(1/n)$ near $\\pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04640","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04640/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":"2606.04640","created_at":"2026-06-04T01:09:22.650794+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04640v1","created_at":"2026-06-04T01:09:22.650794+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04640","created_at":"2026-06-04T01:09:22.650794+00:00"},{"alias_kind":"pith_short_12","alias_value":"MH2K5CPCJX5C","created_at":"2026-06-04T01:09:22.650794+00:00"},{"alias_kind":"pith_short_16","alias_value":"MH2K5CPCJX5CLHM4","created_at":"2026-06-04T01:09:22.650794+00:00"},{"alias_kind":"pith_short_8","alias_value":"MH2K5CPC","created_at":"2026-06-04T01:09:22.650794+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/MH2K5CPCJX5CLHM4O3X5DJ3RBY","json":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY.json","graph_json":"https://pith.science/api/pith-number/MH2K5CPCJX5CLHM4O3X5DJ3RBY/graph.json","events_json":"https://pith.science/api/pith-number/MH2K5CPCJX5CLHM4O3X5DJ3RBY/events.json","paper":"https://pith.science/paper/MH2K5CPC"},"agent_actions":{"view_html":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY","download_json":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY.json","view_paper":"https://pith.science/paper/MH2K5CPC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04640&json=true","fetch_graph":"https://pith.science/api/pith-number/MH2K5CPCJX5CLHM4O3X5DJ3RBY/graph.json","fetch_events":"https://pith.science/api/pith-number/MH2K5CPCJX5CLHM4O3X5DJ3RBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/action/storage_attestation","attest_author":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/action/author_attestation","sign_citation":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/action/citation_signature","submit_replication":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/action/replication_record"}},"created_at":"2026-06-04T01:09:22.650794+00:00","updated_at":"2026-06-04T01:09:22.650794+00:00"}