{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:26X4JH2ZY46OCKL23S2P5VN4U4","short_pith_number":"pith:26X4JH2Z","schema_version":"1.0","canonical_sha256":"d7afc49f59c73ce1297adcb4fed5bca7061f62da645b1c5a9e1f2866b3418887","source":{"kind":"arxiv","id":"1906.05508","version":1},"attestation_state":"computed","paper":{"title":"On simultaneous rational approximation to a real number and its integral powers, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dmitry Badziahin, Yann Bugeaud","submitted_at":"2019-06-13T06:54:13Z","abstract_excerpt":"For a positive integer $n$ and a real number $\\xi$, let $\\lambda_n (\\xi)$ denote the supremum of the real numbers $\\lambda$ for which there are arbitrarily large positive integers $q$ such that $|| q \\xi ||, || q \\xi^2 ||, \\ldots , ||q \\xi^n||$ are all less than $q^{-\\lambda}$. Here, $|| \\cdot ||$ denotes the distance to the nearest integer. We establish new results on the Hausdorff dimension of the set of real numbers $\\xi$ such that $\\lambda_n (\\xi)$ is equal (or greater than or equal) to a given value."},"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":"1906.05508","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-13T06:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"7dbaedb1b1528e24ecf96b79e47cb420950b15666b5437efe18c2e2b60a5f63d","abstract_canon_sha256":"64538a8af62f50a95ab1da49bb23c7f1edfd7cb5616f13f82bc821bb14c4d9df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:25.194430Z","signature_b64":"eV3XMMOUw4CK43Jgb+GKti/HnrZqY/3DID/G57cjFyr/lCgIni3SUMW3KCMDUwr4n2ixlnRxRXhK8ORbIc2QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7afc49f59c73ce1297adcb4fed5bca7061f62da645b1c5a9e1f2866b3418887","last_reissued_at":"2026-05-17T23:43:25.194017Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:25.194017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On simultaneous rational approximation to a real number and its integral powers, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dmitry Badziahin, Yann Bugeaud","submitted_at":"2019-06-13T06:54:13Z","abstract_excerpt":"For a positive integer $n$ and a real number $\\xi$, let $\\lambda_n (\\xi)$ denote the supremum of the real numbers $\\lambda$ for which there are arbitrarily large positive integers $q$ such that $|| q \\xi ||, || q \\xi^2 ||, \\ldots , ||q \\xi^n||$ are all less than $q^{-\\lambda}$. Here, $|| \\cdot ||$ denotes the distance to the nearest integer. We establish new results on the Hausdorff dimension of the set of real numbers $\\xi$ such that $\\lambda_n (\\xi)$ is equal (or greater than or equal) to a given value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05508","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":"1906.05508","created_at":"2026-05-17T23:43:25.194075+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.05508v1","created_at":"2026-05-17T23:43:25.194075+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05508","created_at":"2026-05-17T23:43:25.194075+00:00"},{"alias_kind":"pith_short_12","alias_value":"26X4JH2ZY46O","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"26X4JH2ZY46OCKL2","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"26X4JH2Z","created_at":"2026-05-18T12:33:07.085635+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/26X4JH2ZY46OCKL23S2P5VN4U4","json":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4.json","graph_json":"https://pith.science/api/pith-number/26X4JH2ZY46OCKL23S2P5VN4U4/graph.json","events_json":"https://pith.science/api/pith-number/26X4JH2ZY46OCKL23S2P5VN4U4/events.json","paper":"https://pith.science/paper/26X4JH2Z"},"agent_actions":{"view_html":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4","download_json":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4.json","view_paper":"https://pith.science/paper/26X4JH2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.05508&json=true","fetch_graph":"https://pith.science/api/pith-number/26X4JH2ZY46OCKL23S2P5VN4U4/graph.json","fetch_events":"https://pith.science/api/pith-number/26X4JH2ZY46OCKL23S2P5VN4U4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4/action/storage_attestation","attest_author":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4/action/author_attestation","sign_citation":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4/action/citation_signature","submit_replication":"https://pith.science/pith/26X4JH2ZY46OCKL23S2P5VN4U4/action/replication_record"}},"created_at":"2026-05-17T23:43:25.194075+00:00","updated_at":"2026-05-17T23:43:25.194075+00:00"}