{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QACRTEBVCOMUM5WJG566LZQXQK","short_pith_number":"pith:QACRTEBV","schema_version":"1.0","canonical_sha256":"800519903513994676c9377de5e61782a82d1acb1280d4225a2d3ee6ae595efc","source":{"kind":"arxiv","id":"1608.04326","version":2},"attestation_state":"computed","paper":{"title":"A remark on the extreme value theory for continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kunkun Song, Lulu Fang","submitted_at":"2016-08-15T16:55:13Z","abstract_excerpt":"Let $x$ be a irrational number in the unit interval and denote by its continued fraction expansion $[a_1(x), a_2(x), \\cdots, a_n(x), \\cdots]$. For any $n \\geq 1$, write $T_n(x) = \\max_{1 \\leq k \\leq n}\\{a_k(x)\\}$. We are interested in the Hausdorff dimension of the fractal set \\[ E_\\phi = \\left\\{x \\in (0,1): \\lim_{n \\to \\infty} \\frac{T_n(x)}{\\phi(n)} =1\\right\\}, \\] where $\\phi$ is a positive function defined on $\\mathbb{N}$ with $\\phi(n) \\to \\infty$ as $n \\to \\infty$. Some partial results have been obtained by Wu and Xu, Liao and Rams, and Ma. In the present paper, we further study this topic "},"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":"1608.04326","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-15T16:55:13Z","cross_cats_sorted":[],"title_canon_sha256":"8e770a5d9652708143b541b5d6bd560c45bcaf2412e117356255da7cdf3f9193","abstract_canon_sha256":"dbee18275cc7db2ea7b32d559de63c4c5a7f0181ec5a6c1574be2df5db10766c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.451451Z","signature_b64":"MJvoYq4Re1wGXG8ZIafwm73IM39H8f6JuhJeca9Lgy3g3FF91cbDDwdIybHBRzVRZO3/lBWSTYVO0fJebA8aDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"800519903513994676c9377de5e61782a82d1acb1280d4225a2d3ee6ae595efc","last_reissued_at":"2026-05-18T01:07:50.450968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.450968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on the extreme value theory for continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kunkun Song, Lulu Fang","submitted_at":"2016-08-15T16:55:13Z","abstract_excerpt":"Let $x$ be a irrational number in the unit interval and denote by its continued fraction expansion $[a_1(x), a_2(x), \\cdots, a_n(x), \\cdots]$. For any $n \\geq 1$, write $T_n(x) = \\max_{1 \\leq k \\leq n}\\{a_k(x)\\}$. We are interested in the Hausdorff dimension of the fractal set \\[ E_\\phi = \\left\\{x \\in (0,1): \\lim_{n \\to \\infty} \\frac{T_n(x)}{\\phi(n)} =1\\right\\}, \\] where $\\phi$ is a positive function defined on $\\mathbb{N}$ with $\\phi(n) \\to \\infty$ as $n \\to \\infty$. Some partial results have been obtained by Wu and Xu, Liao and Rams, and Ma. In the present paper, we further study this topic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04326","kind":"arxiv","version":2},"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":"1608.04326","created_at":"2026-05-18T01:07:50.451044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04326v2","created_at":"2026-05-18T01:07:50.451044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04326","created_at":"2026-05-18T01:07:50.451044+00:00"},{"alias_kind":"pith_short_12","alias_value":"QACRTEBVCOMU","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QACRTEBVCOMUM5WJ","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QACRTEBV","created_at":"2026-05-18T12:30:39.010887+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/QACRTEBVCOMUM5WJG566LZQXQK","json":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK.json","graph_json":"https://pith.science/api/pith-number/QACRTEBVCOMUM5WJG566LZQXQK/graph.json","events_json":"https://pith.science/api/pith-number/QACRTEBVCOMUM5WJG566LZQXQK/events.json","paper":"https://pith.science/paper/QACRTEBV"},"agent_actions":{"view_html":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK","download_json":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK.json","view_paper":"https://pith.science/paper/QACRTEBV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04326&json=true","fetch_graph":"https://pith.science/api/pith-number/QACRTEBVCOMUM5WJG566LZQXQK/graph.json","fetch_events":"https://pith.science/api/pith-number/QACRTEBVCOMUM5WJG566LZQXQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK/action/storage_attestation","attest_author":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK/action/author_attestation","sign_citation":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK/action/citation_signature","submit_replication":"https://pith.science/pith/QACRTEBVCOMUM5WJG566LZQXQK/action/replication_record"}},"created_at":"2026-05-18T01:07:50.451044+00:00","updated_at":"2026-05-18T01:07:50.451044+00:00"}