{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:VF3CJGQ2G2I3LYZPMDDQRM5LA4","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":"0ca098e954fe69e828e2cfec9dfb3ebcc1f1b57cab0d86e573992b7843df0a18","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.FA","submitted_at":"2005-08-27T10:20:36Z","title_canon_sha256":"fe4b41007302d0468a0c65023b6d2224acf8aa16b2f95ce29cb042c9a71fe6eb"},"schema_version":"1.0","source":{"id":"math/0508544","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0508544","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0508544v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0508544","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"VF3CJGQ2G2I3","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"VF3CJGQ2G2I3LYZP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"VF3CJGQ2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:64c475f17360510d4ec64cd40988c67f6824525b4edaba77785cbb24a651347c","target":"graph","created_at":"2026-05-18T01:05:23Z","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"},"paper":{"abstract_excerpt":"First we give here a simple proof of a remarkable result of Videnskii and Shirokov: let $B$ be a Blaschke product with $n$ zeros, then there exists an outer function $\\phi, \\phi(0)=1$, such that $\\|(B\\phi)'\\| \\leq C n$, where $C$ is an absolute constant. Then we apply this result to a certain problem of finding the asymptotic of orthogonal polynomials.","authors_text":"A. Volberg, F. Peherstorfer, P. Yuditskii","cross_cats":["math.SP"],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2005-08-27T10:20:36Z","title":"Asymptotics of orthogonal polynomials beyond the scope of Szego's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0508544","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":"sha256:091e23466118ba51795bad9705d88c64533310e086b646a817a59d570c72e6ca","target":"record","created_at":"2026-05-18T01:05:23Z","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":"0ca098e954fe69e828e2cfec9dfb3ebcc1f1b57cab0d86e573992b7843df0a18","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.FA","submitted_at":"2005-08-27T10:20:36Z","title_canon_sha256":"fe4b41007302d0468a0c65023b6d2224acf8aa16b2f95ce29cb042c9a71fe6eb"},"schema_version":"1.0","source":{"id":"math/0508544","kind":"arxiv","version":1}},"canonical_sha256":"a976249a1a3691b5e32f60c708b3ab073f16d247ae62935efab749c6cc5b37b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a976249a1a3691b5e32f60c708b3ab073f16d247ae62935efab749c6cc5b37b7","first_computed_at":"2026-05-18T01:05:23.226687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.226687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lv0+eMKZGqL4UVul9QG+dVNyibjyqTWHXclGeezHx4v3veQIdpPowDJWph+gCkWn6vtLDtmm30Z7K15RwxFzBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.227143Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0508544","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091e23466118ba51795bad9705d88c64533310e086b646a817a59d570c72e6ca","sha256:64c475f17360510d4ec64cd40988c67f6824525b4edaba77785cbb24a651347c"],"state_sha256":"336cffdba9b28e1fb5667aba3d003bb0a2360a503fa7fdafb03a15a018b0a8f2"}