{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:6ZYF33OW2VDMO5YALOI3ARERXP","short_pith_number":"pith:6ZYF33OW","schema_version":"1.0","canonical_sha256":"f6705dedd6d546c777005b91b04491bbfb20f76f1ea1cf8e95ebc2f125b416db","source":{"kind":"arxiv","id":"1905.13349","version":1},"attestation_state":"computed","paper":{"title":"Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Ali Pirhadi","submitted_at":"2019-05-30T23:10:23Z","abstract_excerpt":"It is well known that the expected number of real zeros of a random cosine polynomial $ V_n(x) = \\sum_ {j=0} ^{n} a_j \\cos (j x) , \\ x \\in (0,2\\pi) $, with the $ a_j $ being standard Gaussian i.i.d. random variables is asymptotically $ 2n / \\sqrt{3} $. On the other hand, some of the previous works on the random cosine polynomials with dependent coefficients show that such polynomials have at least $ 2n / \\sqrt{3} $ expected real zeros lying in one period. In this paper we investigate two classes of random cosine polynomials with pairwise equal blocks of coefficients. First, we prove that a ran"},"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":"1905.13349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-05-30T23:10:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"fadbe87d1a444a2eb7e63f23b2cb36d032a1e43766d9e2ca2ef030908ac62d26","abstract_canon_sha256":"3d349e77b8ec0b47f6639c5dd4791a505068eba9f5a4bd19e50e5cf009af3236"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:07.559354Z","signature_b64":"mglhx3PWt9rmRZPBIzO4fNZ3h0g/Ldn+dPfReJe3D+UN3KdADzinCqwr+cYnyk5uAcJgKJ+nO1V6BQqh3LgAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6705dedd6d546c777005b91b04491bbfb20f76f1ea1cf8e95ebc2f125b416db","last_reissued_at":"2026-07-04T23:59:07.558877Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:07.558877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CA","authors_text":"Ali Pirhadi","submitted_at":"2019-05-30T23:10:23Z","abstract_excerpt":"It is well known that the expected number of real zeros of a random cosine polynomial $ V_n(x) = \\sum_ {j=0} ^{n} a_j \\cos (j x) , \\ x \\in (0,2\\pi) $, with the $ a_j $ being standard Gaussian i.i.d. random variables is asymptotically $ 2n / \\sqrt{3} $. On the other hand, some of the previous works on the random cosine polynomials with dependent coefficients show that such polynomials have at least $ 2n / \\sqrt{3} $ expected real zeros lying in one period. In this paper we investigate two classes of random cosine polynomials with pairwise equal blocks of coefficients. First, we prove that a ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13349","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/1905.13349/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.13349","created_at":"2026-07-04T23:59:07.558942+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.13349v1","created_at":"2026-07-04T23:59:07.558942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.13349","created_at":"2026-07-04T23:59:07.558942+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ZYF33OW2VDM","created_at":"2026-07-04T23:59:07.558942+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ZYF33OW2VDMO5YA","created_at":"2026-07-04T23:59:07.558942+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ZYF33OW","created_at":"2026-07-04T23:59:07.558942+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.08154","citing_title":"Real zeros of random cosine polynomials with palindromic blocks of coefficients","ref_index":23,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP","json":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP.json","graph_json":"https://pith.science/api/pith-number/6ZYF33OW2VDMO5YALOI3ARERXP/graph.json","events_json":"https://pith.science/api/pith-number/6ZYF33OW2VDMO5YALOI3ARERXP/events.json","paper":"https://pith.science/paper/6ZYF33OW"},"agent_actions":{"view_html":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP","download_json":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP.json","view_paper":"https://pith.science/paper/6ZYF33OW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.13349&json=true","fetch_graph":"https://pith.science/api/pith-number/6ZYF33OW2VDMO5YALOI3ARERXP/graph.json","fetch_events":"https://pith.science/api/pith-number/6ZYF33OW2VDMO5YALOI3ARERXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP/action/storage_attestation","attest_author":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP/action/author_attestation","sign_citation":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP/action/citation_signature","submit_replication":"https://pith.science/pith/6ZYF33OW2VDMO5YALOI3ARERXP/action/replication_record"}},"created_at":"2026-07-04T23:59:07.558942+00:00","updated_at":"2026-07-04T23:59:07.558942+00:00"}