{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MH2K5CPCJX5CLHM4O3X5DJ3RBY","short_pith_number":"pith:MH2K5CPC","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"},"canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","source":{"kind":"arxiv","id":"2606.04640","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04640","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04640v1","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04640","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"MH2K5CPCJX5C","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"MH2K5CPCJX5CLHM4","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"MH2K5CPC","created_at":"2026-06-04T01:09:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MH2K5CPCJX5CLHM4O3X5DJ3RBY","target":"record","payload":{"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"},"canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","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"},"source_kind":"arxiv","source_id":"2606.04640","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2RsIuo73I95kVw1dXfIZ1nCkRcTD4QFAZqhVCQe6Nq8oRysRabpZL19t5MWGnA11MRTHVKYPA+Di2JuSwdSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:23:29.891732Z"},"content_sha256":"b9b9f2d5fa478387d6eebca1a5fc75a90724f9a8e79d229a5a61c6f81500f88c","schema_version":"1.0","event_id":"sha256:b9b9f2d5fa478387d6eebca1a5fc75a90724f9a8e79d229a5a61c6f81500f88c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MH2K5CPCJX5CLHM4O3X5DJ3RBY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uc5uEIYjqL2tMFAx9R6Vaw+vc7mhEi0D1s3iAFgouwBU3UIE7MHHLq/BVUQgQTmoNO9/O6CJi4jUqARGX0LWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T11:23:29.892106Z"},"content_sha256":"3bb22c016539d3209802d247ee82583d09740ce7d4270a4f2fa95c1a50313a77","schema_version":"1.0","event_id":"sha256:3bb22c016539d3209802d247ee82583d09740ce7d4270a4f2fa95c1a50313a77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/bundle.json","state_url":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T11:23:29Z","links":{"resolver":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY","bundle":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/bundle.json","state":"https://pith.science/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MH2K5CPCJX5CLHM4O3X5DJ3RBY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MH2K5CPCJX5CLHM4O3X5DJ3RBY","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":"443650ce3b2350ed957a17d812ece23fe1def406c911e8e6019ae4e2ca2ad581","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-06-03T09:09:52Z","title_canon_sha256":"5d2900d68bd74c280c33117b8d2f18fd8e796369a17fe209a96186036ff1c0a6"},"schema_version":"1.0","source":{"id":"2606.04640","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04640","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04640v1","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04640","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"MH2K5CPCJX5C","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"MH2K5CPCJX5CLHM4","created_at":"2026-06-04T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"MH2K5CPC","created_at":"2026-06-04T01:09:22Z"}],"graph_snapshots":[{"event_id":"sha256:3bb22c016539d3209802d247ee82583d09740ce7d4270a4f2fa95c1a50313a77","target":"graph","created_at":"2026-06-04T01:09:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.04640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Artur Nicolau, Roman Bessonov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-06-03T09:09:52Z","title":"From local to global asymptotic behaviour of orthogonal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04640","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:b9b9f2d5fa478387d6eebca1a5fc75a90724f9a8e79d229a5a61c6f81500f88c","target":"record","created_at":"2026-06-04T01:09:22Z","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":"443650ce3b2350ed957a17d812ece23fe1def406c911e8e6019ae4e2ca2ad581","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-06-03T09:09:52Z","title_canon_sha256":"5d2900d68bd74c280c33117b8d2f18fd8e796369a17fe209a96186036ff1c0a6"},"schema_version":"1.0","source":{"id":"2606.04640","kind":"arxiv","version":1}},"canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61f4ae89e24dfa259d9c76efd1a7710e3fb8943f49b93ea948563a44ed298553","first_computed_at":"2026-06-04T01:09:22.650579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:22.650579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Yku+IPnVy1ApPmyB1ufxVKNV7QWTb4xhD9WsdO4xhlNaRTGP8m9fuYGAPzzi6JoxVOVJb0Pb+ndcW4OGwSeDQ==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:22.652094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04640","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9b9f2d5fa478387d6eebca1a5fc75a90724f9a8e79d229a5a61c6f81500f88c","sha256:3bb22c016539d3209802d247ee82583d09740ce7d4270a4f2fa95c1a50313a77"],"state_sha256":"8a37aaaa8019c00dedff2972fe3c5a99e554959dfd2fe4234b2d6602baa15918"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ts7eyNtwN391ZVwGg1ORPgFPHmaB7C2LJHOKEu4geTridthDKWQoaIPYIB0B5oTVbZsi9nK50nuKiWmGdFXnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T11:23:29.894205Z","bundle_sha256":"a58616c8187bc5977b3c38f29a7daee4b28dc2056453751b794da54e0571ce8c"}}