{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EDX6FGZ4TQ44WTBQKXMIK43SQP","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":"a3927e202749cef81db52f65fb0628df37c33b2ef8de8c12a5859b99b5eab44f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-10T19:29:48Z","title_canon_sha256":"1e0778bd583a9f592eb53f25eff8c8dfb42551c7d2039e42b0b5c81aae0417de"},"schema_version":"1.0","source":{"id":"1107.1887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1887","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1887v1","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1887","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"EDX6FGZ4TQ44","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EDX6FGZ4TQ44WTBQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EDX6FGZ4","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:b3b3b6602ac22df059dfeb893d5552468c008b0972a1fb0b2b3e5cc192f4a595","target":"graph","created_at":"2026-05-18T04:18:33Z","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":"Complex-valued periodic sequences, u, constructed by Goran Bjorck, are analyzed with regard to the behavior of their discrete periodic narrow-band ambiguity functions A_p(u). The Bjorck sequences, which are defined on Z/pZ for p>2 prime, are unimodular and have zero autocorrelation on (Z/pZ)\\{0}. These two properties give rise to the acronym, CAZAC, to refer to constant amplitude zero autocorrelation sequences. The bound proven is |A_p(u)| \\leq 2/\\sqrt{p} + 4/p outside of (0,0), and this is of optimal magnitude given the constraint that u is a CAZAC sequence. The proof requires the full power ","authors_text":"John J. Benedetto, Joseph T. Woodworth, Robert L. Benedetto","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-10T19:29:48Z","title":"Optimal ambiguity functions and Weil's exponential sum bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1887","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":"sha256:6cef5edc4cdb9ea064598e569909e86e6f5d9897a954f6958a4bac9e9e74d85c","target":"record","created_at":"2026-05-18T04:18:33Z","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":"a3927e202749cef81db52f65fb0628df37c33b2ef8de8c12a5859b99b5eab44f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-10T19:29:48Z","title_canon_sha256":"1e0778bd583a9f592eb53f25eff8c8dfb42551c7d2039e42b0b5c81aae0417de"},"schema_version":"1.0","source":{"id":"1107.1887","kind":"arxiv","version":1}},"canonical_sha256":"20efe29b3c9c39cb4c3055d885737283e9a27335f973233e87dd1b2d78a139c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20efe29b3c9c39cb4c3055d885737283e9a27335f973233e87dd1b2d78a139c2","first_computed_at":"2026-05-18T04:18:33.943674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:33.943674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d71LLoX4/4VOjGYyEw42xC99Dfe4UVDuVr6ae3/di1x2Qp1xCjMq40gNhFcNY1S3SU40TiLlVWMYzOr1XVtyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:33.944261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cef5edc4cdb9ea064598e569909e86e6f5d9897a954f6958a4bac9e9e74d85c","sha256:b3b3b6602ac22df059dfeb893d5552468c008b0972a1fb0b2b3e5cc192f4a595"],"state_sha256":"e5482da70e37ed4c2d7ba52d133e4c1247bd4dbfc9ca8249b8a3fc6fe2d14b03"}