{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XZRAIPD3IYLRZHZTJQNHCBPSYT","short_pith_number":"pith:XZRAIPD3","schema_version":"1.0","canonical_sha256":"be62043c7b46171c9f334c1a7105f2c4e874502421844c813676fd8a26e5ec1a","source":{"kind":"arxiv","id":"1601.02202","version":1},"attestation_state":"computed","paper":{"title":"Limit theorems related to beta-expansion and continued fraction expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Bing Li, Lulu Fang, Min Wu","submitted_at":"2016-01-10T11:52:40Z","abstract_excerpt":"Let $\\beta > 1$ be a real number and $x \\in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\\beta$-expansion of $x$ ($n \\in \\mathbb{N}$). In this paper, we show a central limit theorem and a law of the iterated logarithm for the random variables sequence $\\{k_n, n \\geq 1\\}$, which generalize the results of Faivre and Wu respectively from $\\beta =10$ to any $\\beta >1$."},"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":"1601.02202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-10T11:52:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"3c27ba0ffc88a4c78a39c06773288686cedf85d87c1f897b51a46d10e90d687b","abstract_canon_sha256":"bf28aca1faf11abb5e0482981fffd6c6962121bdc9f1bb2eefbb9fe457fbe323"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:35.116741Z","signature_b64":"QhTbX9b9zbKjPy2Wjyq/+XJQEqHNaRbElpObXAAnWX3OJ9zf9Z8B2kKtRPdsPd2jkKcALUCHRDBQFPMvZV4DDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be62043c7b46171c9f334c1a7105f2c4e874502421844c813676fd8a26e5ec1a","last_reissued_at":"2026-05-18T01:11:35.116236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:35.116236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit theorems related to beta-expansion and continued fraction expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Bing Li, Lulu Fang, Min Wu","submitted_at":"2016-01-10T11:52:40Z","abstract_excerpt":"Let $\\beta > 1$ be a real number and $x \\in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $\\beta$-expansion of $x$ ($n \\in \\mathbb{N}$). In this paper, we show a central limit theorem and a law of the iterated logarithm for the random variables sequence $\\{k_n, n \\geq 1\\}$, which generalize the results of Faivre and Wu respectively from $\\beta =10$ to any $\\beta >1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02202","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":"1601.02202","created_at":"2026-05-18T01:11:35.116311+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.02202v1","created_at":"2026-05-18T01:11:35.116311+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02202","created_at":"2026-05-18T01:11:35.116311+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZRAIPD3IYLR","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZRAIPD3IYLRZHZT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZRAIPD3","created_at":"2026-05-18T12:30:51.357362+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/XZRAIPD3IYLRZHZTJQNHCBPSYT","json":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT.json","graph_json":"https://pith.science/api/pith-number/XZRAIPD3IYLRZHZTJQNHCBPSYT/graph.json","events_json":"https://pith.science/api/pith-number/XZRAIPD3IYLRZHZTJQNHCBPSYT/events.json","paper":"https://pith.science/paper/XZRAIPD3"},"agent_actions":{"view_html":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT","download_json":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT.json","view_paper":"https://pith.science/paper/XZRAIPD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.02202&json=true","fetch_graph":"https://pith.science/api/pith-number/XZRAIPD3IYLRZHZTJQNHCBPSYT/graph.json","fetch_events":"https://pith.science/api/pith-number/XZRAIPD3IYLRZHZTJQNHCBPSYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT/action/storage_attestation","attest_author":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT/action/author_attestation","sign_citation":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT/action/citation_signature","submit_replication":"https://pith.science/pith/XZRAIPD3IYLRZHZTJQNHCBPSYT/action/replication_record"}},"created_at":"2026-05-18T01:11:35.116311+00:00","updated_at":"2026-05-18T01:11:35.116311+00:00"}