{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LWVZMCXNYCKQZCETRK7FFGKGD3","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":"e1d5e6bf7a75e214c8d9430537c364c86a5193f118cea5f5e1c4ea80d0233af1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-04T14:17:23Z","title_canon_sha256":"184c0cf5af46360e9ce5b6c050f5fd5bc0b65a76b2109545d7f19df4337453e7"},"schema_version":"1.0","source":{"id":"1006.0900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0900","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0900v2","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0900","created_at":"2026-05-18T04:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"LWVZMCXNYCKQ","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LWVZMCXNYCKQZCET","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LWVZMCXN","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:be8d70fdcb038fba2b138163e56b4c99c79ef6ec04b0f000e9e5256d87ab0713","target":"graph","created_at":"2026-05-18T04:41:53Z","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":"We show that for many families of OPUC, one has $||\\varphi'_n||_2/n -> 1$, a condition we call normal behavior. We prove that this implies $|\\alpha_n| -> 0$ and that it holds if the sequence $\\alpha_n$ is in $\\ell^1$. We also prove it is true for many sparse sequences. On the other hand, it is often destroyed by the insertion of a mass point.","authors_text":"Andrei Martinez-Finkelshtein, Barry Simon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-04T14:17:23Z","title":"Asymptotics of the L^2 Norm of Derivatives of OPUC"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0900","kind":"arxiv","version":2},"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:ca0b85bcc0c45d1c2a273179d634d9daca349b3d744d6c638819f325addc828d","target":"record","created_at":"2026-05-18T04:41:53Z","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":"e1d5e6bf7a75e214c8d9430537c364c86a5193f118cea5f5e1c4ea80d0233af1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-04T14:17:23Z","title_canon_sha256":"184c0cf5af46360e9ce5b6c050f5fd5bc0b65a76b2109545d7f19df4337453e7"},"schema_version":"1.0","source":{"id":"1006.0900","kind":"arxiv","version":2}},"canonical_sha256":"5dab960aedc0950c88938abe5299461ec245aef89b26f98b2b22e2747895c180","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dab960aedc0950c88938abe5299461ec245aef89b26f98b2b22e2747895c180","first_computed_at":"2026-05-18T04:41:53.745511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:53.745511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ei/Eh/a7CJTi311xhQkWOU8ASOeIC5hi6oZEzEVktxvLKhrHcT8jSoviX2YDZ2lUxv4QUlKIaz8uosKoHtlbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:53.746004Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0b85bcc0c45d1c2a273179d634d9daca349b3d744d6c638819f325addc828d","sha256:be8d70fdcb038fba2b138163e56b4c99c79ef6ec04b0f000e9e5256d87ab0713"],"state_sha256":"424d3b90d5e67f07c7be28847f96497dd300b233cd76df299e0f43319524371b"}