{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:N3B762DPJSKMJ2443WRYDZRSIC","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":"a6e0f2354307c5f61042ecee07f6284729a891d26a4c412008b26f7d2a5399ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-11T07:49:49Z","title_canon_sha256":"7f394e588668338e94b7f2b2687acd67f005d7a8da4e5b98bdc6d056429c5b24"},"schema_version":"1.0","source":{"id":"1804.03851","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03851","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03851v2","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03851","created_at":"2026-05-18T00:17:37Z"},{"alias_kind":"pith_short_12","alias_value":"N3B762DPJSKM","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"N3B762DPJSKMJ244","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"N3B762DP","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:56069edecb89ec67d05877dc2f96c0109338eee8bcef7d0626276c90ef288bd1","target":"graph","created_at":"2026-05-18T00:17:37Z","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":"For numerical sequences taking values $0$ or complex numbers of modulus $1$, we define Chowla property and Sarnak property. We prove that Chowla property implies Sarnak property. We also prove that for Lebesgue almost every $\\beta>1$, the sequence $(e^{2\\pi \\beta^n})_{n\\in \\mathbb{N}}$ shares Chowla property and consequently is orthogonal to all topological dynamical systems of zero entropy. It is also discussed whether the samples of a given random sequence have Chowla property almost surely. Some dependent random sequences having almost surely Chowla property are constructed.","authors_text":"Ruxi Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-11T07:49:49Z","title":"Construction of some Chowla sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03851","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":"sha256:4b716a7547a5df45f6e35d30ec35598ee7a38e4ab7ca958acc191bf0bf69346a","target":"record","created_at":"2026-05-18T00:17:37Z","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":"a6e0f2354307c5f61042ecee07f6284729a891d26a4c412008b26f7d2a5399ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-11T07:49:49Z","title_canon_sha256":"7f394e588668338e94b7f2b2687acd67f005d7a8da4e5b98bdc6d056429c5b24"},"schema_version":"1.0","source":{"id":"1804.03851","kind":"arxiv","version":2}},"canonical_sha256":"6ec3ff686f4c94c4eb9cdda381e63240a2536c595e9bd88173a23af48e3d8e8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ec3ff686f4c94c4eb9cdda381e63240a2536c595e9bd88173a23af48e3d8e8e","first_computed_at":"2026-05-18T00:17:37.795146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:37.795146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YdF3WmojoY25lYHTqOYUUQfPH/EKed/X94NUboOKyJieMJd6tb8zS1ICTwXh70ya/HDRhjLiyEUJSFlkRpT3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:37.795679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03851","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b716a7547a5df45f6e35d30ec35598ee7a38e4ab7ca958acc191bf0bf69346a","sha256:56069edecb89ec67d05877dc2f96c0109338eee8bcef7d0626276c90ef288bd1"],"state_sha256":"5ec38d5ea54040c6f7d564b3248dfcfad37067774765fd9d4e5cedaf8c5ee5a9"}