{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JM6UVNO4QYGZAYYTARVIHKRHE4","short_pith_number":"pith:JM6UVNO4","schema_version":"1.0","canonical_sha256":"4b3d4ab5dc860d906313046a83aa2727140882388b220667abe20f4462390e91","source":{"kind":"arxiv","id":"1611.03043","version":1},"attestation_state":"computed","paper":{"title":"Pseudorandomness of the Ostrowski sum-of-digits function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2016-11-09T18:42:30Z","abstract_excerpt":"For an irrational $\\alpha\\in(0,1)$, we investigate the Ostrowski sum-of-digits function $\\sigma_\\alpha$. For $\\alpha$ having bounded partial quotients and $\\vartheta\\in\\mathbb R\\setminus\\mathbb Z$, we prove that the function $g:n\\mapsto \\mathrm e(\\vartheta \\sigma_\\alpha(n))$, where $\\mathrm e(x)=\\mathrm e^{2\\pi i x}$, is pseudorandom in the following sense: for all $r\\in\\mathbb N$ the limit \\[\\gamma_r= \\lim_{N\\rightarrow\\infty}\\frac 1N\\sum_{0\\leq n<N}g(n+r)\\overline{g(n)} \\] exists and we have \\[\\lim_{R\\rightarrow\\infty}\\frac 1R\\sum_{0\\leq r<R}\\bigl\\lvert \\gamma_r\\bigr\\rvert^2=0.\\]"},"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":"1611.03043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-09T18:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"3677aa592976ee9af17a7931f3ca80178f35b9dda4893f4be8eb1f133902775d","abstract_canon_sha256":"2f0d07dcb26650751acea5e5827d6e3279310417477312973a8027915192ecc0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:42.750345Z","signature_b64":"rtuqzelrOvVpLeYjQtbqgVjgbCmNvpRUppYP7aM8G1TKKc1oQgBXiKK3wCwItB/YWi6cLDSFSsVIXBT9dhw/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b3d4ab5dc860d906313046a83aa2727140882388b220667abe20f4462390e91","last_reissued_at":"2026-05-18T00:59:42.749844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:42.749844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudorandomness of the Ostrowski sum-of-digits function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Spiegelhofer","submitted_at":"2016-11-09T18:42:30Z","abstract_excerpt":"For an irrational $\\alpha\\in(0,1)$, we investigate the Ostrowski sum-of-digits function $\\sigma_\\alpha$. For $\\alpha$ having bounded partial quotients and $\\vartheta\\in\\mathbb R\\setminus\\mathbb Z$, we prove that the function $g:n\\mapsto \\mathrm e(\\vartheta \\sigma_\\alpha(n))$, where $\\mathrm e(x)=\\mathrm e^{2\\pi i x}$, is pseudorandom in the following sense: for all $r\\in\\mathbb N$ the limit \\[\\gamma_r= \\lim_{N\\rightarrow\\infty}\\frac 1N\\sum_{0\\leq n<N}g(n+r)\\overline{g(n)} \\] exists and we have \\[\\lim_{R\\rightarrow\\infty}\\frac 1R\\sum_{0\\leq r<R}\\bigl\\lvert \\gamma_r\\bigr\\rvert^2=0.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03043","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":"1611.03043","created_at":"2026-05-18T00:59:42.749929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.03043v1","created_at":"2026-05-18T00:59:42.749929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03043","created_at":"2026-05-18T00:59:42.749929+00:00"},{"alias_kind":"pith_short_12","alias_value":"JM6UVNO4QYGZ","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JM6UVNO4QYGZAYYT","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JM6UVNO4","created_at":"2026-05-18T12:30:25.849896+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/JM6UVNO4QYGZAYYTARVIHKRHE4","json":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4.json","graph_json":"https://pith.science/api/pith-number/JM6UVNO4QYGZAYYTARVIHKRHE4/graph.json","events_json":"https://pith.science/api/pith-number/JM6UVNO4QYGZAYYTARVIHKRHE4/events.json","paper":"https://pith.science/paper/JM6UVNO4"},"agent_actions":{"view_html":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4","download_json":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4.json","view_paper":"https://pith.science/paper/JM6UVNO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.03043&json=true","fetch_graph":"https://pith.science/api/pith-number/JM6UVNO4QYGZAYYTARVIHKRHE4/graph.json","fetch_events":"https://pith.science/api/pith-number/JM6UVNO4QYGZAYYTARVIHKRHE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4/action/storage_attestation","attest_author":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4/action/author_attestation","sign_citation":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4/action/citation_signature","submit_replication":"https://pith.science/pith/JM6UVNO4QYGZAYYTARVIHKRHE4/action/replication_record"}},"created_at":"2026-05-18T00:59:42.749929+00:00","updated_at":"2026-05-18T00:59:42.749929+00:00"}