{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:EO2HQA56WSR7ZXDHUV4LXEHDD2","short_pith_number":"pith:EO2HQA56","schema_version":"1.0","canonical_sha256":"23b47803beb4a3fcdc67a578bb90e31eafb30dd18b86e484990a51919bff9f00","source":{"kind":"arxiv","id":"1409.5220","version":1},"attestation_state":"computed","paper":{"title":"Normal number constructions for Cantor series with slowly growing bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Dylan Airey, Joseph Vandehey","submitted_at":"2014-09-18T08:13:53Z","abstract_excerpt":"Let $Q=(q_n)_{n=1}^\\infty$ be a sequence of bases with $q_i\\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both $Q$-normal and $Q$-distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of $Q$, and from this construction we can provide computable constructions of numbers with atypical normality properties."},"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":"1409.5220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-18T08:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"ad422627f70b14a31a43d787e47b25e488b2f19f72f2b797ef59ba56a3a29be8","abstract_canon_sha256":"2036a6bc84e295ddd66c2e1235956ed95d656585f28e65dc670a258d178676a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:30.440545Z","signature_b64":"EwG8v2KLghClQtJx6i9A7q1ywlNMCUTc1Wp9CYMXtzSsFwUEW01mYQCzARhyPL6643MI43ZyOsZcliPxdJnsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23b47803beb4a3fcdc67a578bb90e31eafb30dd18b86e484990a51919bff9f00","last_reissued_at":"2026-05-18T02:42:30.439022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:30.439022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal number constructions for Cantor series with slowly growing bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Dylan Airey, Joseph Vandehey","submitted_at":"2014-09-18T08:13:53Z","abstract_excerpt":"Let $Q=(q_n)_{n=1}^\\infty$ be a sequence of bases with $q_i\\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both $Q$-normal and $Q$-distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of $Q$, and from this construction we can provide computable constructions of numbers with atypical normality properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5220","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":"1409.5220","created_at":"2026-05-18T02:42:30.439685+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.5220v1","created_at":"2026-05-18T02:42:30.439685+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5220","created_at":"2026-05-18T02:42:30.439685+00:00"},{"alias_kind":"pith_short_12","alias_value":"EO2HQA56WSR7","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"EO2HQA56WSR7ZXDH","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"EO2HQA56","created_at":"2026-05-18T12:28:28.263976+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/EO2HQA56WSR7ZXDHUV4LXEHDD2","json":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2.json","graph_json":"https://pith.science/api/pith-number/EO2HQA56WSR7ZXDHUV4LXEHDD2/graph.json","events_json":"https://pith.science/api/pith-number/EO2HQA56WSR7ZXDHUV4LXEHDD2/events.json","paper":"https://pith.science/paper/EO2HQA56"},"agent_actions":{"view_html":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2","download_json":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2.json","view_paper":"https://pith.science/paper/EO2HQA56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.5220&json=true","fetch_graph":"https://pith.science/api/pith-number/EO2HQA56WSR7ZXDHUV4LXEHDD2/graph.json","fetch_events":"https://pith.science/api/pith-number/EO2HQA56WSR7ZXDHUV4LXEHDD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2/action/storage_attestation","attest_author":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2/action/author_attestation","sign_citation":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2/action/citation_signature","submit_replication":"https://pith.science/pith/EO2HQA56WSR7ZXDHUV4LXEHDD2/action/replication_record"}},"created_at":"2026-05-18T02:42:30.439685+00:00","updated_at":"2026-05-18T02:42:30.439685+00:00"}