{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:EDX6FGZ4TQ44WTBQKXMIK43SQP","short_pith_number":"pith:EDX6FGZ4","schema_version":"1.0","canonical_sha256":"20efe29b3c9c39cb4c3055d885737283e9a27335f973233e87dd1b2d78a139c2","source":{"kind":"arxiv","id":"1107.1887","version":1},"attestation_state":"computed","paper":{"title":"Optimal ambiguity functions and Weil's exponential sum bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"John J. Benedetto, Joseph T. Woodworth, Robert L. Benedetto","submitted_at":"2011-07-10T19:29:48Z","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 "},"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":"1107.1887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-10T19:29:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1e0778bd583a9f592eb53f25eff8c8dfb42551c7d2039e42b0b5c81aae0417de","abstract_canon_sha256":"a3927e202749cef81db52f65fb0628df37c33b2ef8de8c12a5859b99b5eab44f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.944261Z","signature_b64":"d71LLoX4/4VOjGYyEw42xC99Dfe4UVDuVr6ae3/di1x2Qp1xCjMq40gNhFcNY1S3SU40TiLlVWMYzOr1XVtyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20efe29b3c9c39cb4c3055d885737283e9a27335f973233e87dd1b2d78a139c2","last_reissued_at":"2026-05-18T04:18:33.943674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.943674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal ambiguity functions and Weil's exponential sum bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"John J. Benedetto, Joseph T. Woodworth, Robert L. Benedetto","submitted_at":"2011-07-10T19:29:48Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1887","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":""},"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":"1107.1887","created_at":"2026-05-18T04:18:33.943757+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.1887v1","created_at":"2026-05-18T04:18:33.943757+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1887","created_at":"2026-05-18T04:18:33.943757+00:00"},{"alias_kind":"pith_short_12","alias_value":"EDX6FGZ4TQ44","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"EDX6FGZ4TQ44WTBQ","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"EDX6FGZ4","created_at":"2026-05-18T12:26:28.662955+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/EDX6FGZ4TQ44WTBQKXMIK43SQP","json":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP.json","graph_json":"https://pith.science/api/pith-number/EDX6FGZ4TQ44WTBQKXMIK43SQP/graph.json","events_json":"https://pith.science/api/pith-number/EDX6FGZ4TQ44WTBQKXMIK43SQP/events.json","paper":"https://pith.science/paper/EDX6FGZ4"},"agent_actions":{"view_html":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP","download_json":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP.json","view_paper":"https://pith.science/paper/EDX6FGZ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.1887&json=true","fetch_graph":"https://pith.science/api/pith-number/EDX6FGZ4TQ44WTBQKXMIK43SQP/graph.json","fetch_events":"https://pith.science/api/pith-number/EDX6FGZ4TQ44WTBQKXMIK43SQP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP/action/storage_attestation","attest_author":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP/action/author_attestation","sign_citation":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP/action/citation_signature","submit_replication":"https://pith.science/pith/EDX6FGZ4TQ44WTBQKXMIK43SQP/action/replication_record"}},"created_at":"2026-05-18T04:18:33.943757+00:00","updated_at":"2026-05-18T04:18:33.943757+00:00"}