{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JACJS3I7HAPKNZKDUOXUGFOVO6","short_pith_number":"pith:JACJS3I7","schema_version":"1.0","canonical_sha256":"4804996d1f381ea6e543a3af4315d57797b880aa0795fa2a42999493ebb4f3d5","source":{"kind":"arxiv","id":"1404.1889","version":3},"attestation_state":"computed","paper":{"title":"Uniform Diophantine approximation related to $b$-ary and $\\beta$-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Yann Bugeaud (IRMA)","submitted_at":"2014-04-07T19:15:40Z","abstract_excerpt":"Let $b\\geq 2$ be an integer and $\\hv$ a real number. Among other results, we compute the Hausdorff dimension of the set of real numbers $\\xi$ with the property that, for every sufficiently large integer $N$, there exists an integer $n$ such that $1 \\le n \\le N$ and the distance between $b^n \\xi$ and its nearest integer is at most equal to $b^{-\\hv N}$. We further solve the same question when replacing $b^n\\xi$ by $T^n_\\beta \\xi$, where $T_\\beta$ denotes the classical $\\beta$-transformation."},"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":"1404.1889","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-07T19:15:40Z","cross_cats_sorted":[],"title_canon_sha256":"e746d80da6562c6c593da7fcc066d1a67e92e5c1151ddeaaac1d6a52f06a46e2","abstract_canon_sha256":"7ad6da5d59c92e8b091f0e3d3bad56211049884b236959e83bbe415bfb5c448f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:40.327346Z","signature_b64":"/lte8Np69g5j0I7f7pZOpEIZJI2/xfp8xuxTvJFHnt5jMaDSpccxlFQK3xdy9Z7xehNXtjo1IQ68yuD8gL9aCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4804996d1f381ea6e543a3af4315d57797b880aa0795fa2a42999493ebb4f3d5","last_reissued_at":"2026-05-18T01:23:40.326713Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:40.326713Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform Diophantine approximation related to $b$-ary and $\\beta$-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lingmin Liao (LAMA), Yann Bugeaud (IRMA)","submitted_at":"2014-04-07T19:15:40Z","abstract_excerpt":"Let $b\\geq 2$ be an integer and $\\hv$ a real number. Among other results, we compute the Hausdorff dimension of the set of real numbers $\\xi$ with the property that, for every sufficiently large integer $N$, there exists an integer $n$ such that $1 \\le n \\le N$ and the distance between $b^n \\xi$ and its nearest integer is at most equal to $b^{-\\hv N}$. We further solve the same question when replacing $b^n\\xi$ by $T^n_\\beta \\xi$, where $T_\\beta$ denotes the classical $\\beta$-transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1889","kind":"arxiv","version":3},"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":"1404.1889","created_at":"2026-05-18T01:23:40.326823+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1889v3","created_at":"2026-05-18T01:23:40.326823+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1889","created_at":"2026-05-18T01:23:40.326823+00:00"},{"alias_kind":"pith_short_12","alias_value":"JACJS3I7HAPK","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JACJS3I7HAPKNZKD","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JACJS3I7","created_at":"2026-05-18T12:28:33.132498+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/JACJS3I7HAPKNZKDUOXUGFOVO6","json":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6.json","graph_json":"https://pith.science/api/pith-number/JACJS3I7HAPKNZKDUOXUGFOVO6/graph.json","events_json":"https://pith.science/api/pith-number/JACJS3I7HAPKNZKDUOXUGFOVO6/events.json","paper":"https://pith.science/paper/JACJS3I7"},"agent_actions":{"view_html":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6","download_json":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6.json","view_paper":"https://pith.science/paper/JACJS3I7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1889&json=true","fetch_graph":"https://pith.science/api/pith-number/JACJS3I7HAPKNZKDUOXUGFOVO6/graph.json","fetch_events":"https://pith.science/api/pith-number/JACJS3I7HAPKNZKDUOXUGFOVO6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6/action/storage_attestation","attest_author":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6/action/author_attestation","sign_citation":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6/action/citation_signature","submit_replication":"https://pith.science/pith/JACJS3I7HAPKNZKDUOXUGFOVO6/action/replication_record"}},"created_at":"2026-05-18T01:23:40.326823+00:00","updated_at":"2026-05-18T01:23:40.326823+00:00"}