{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:URPZWFIMCYYVA6CMV664VMIXFE","short_pith_number":"pith:URPZWFIM","schema_version":"1.0","canonical_sha256":"a45f9b150c163150784cafbdcab1172900822a651391223ec418fb8e99d49c48","source":{"kind":"arxiv","id":"0911.1485","version":2},"attestation_state":"computed","paper":{"title":"Construction of normal numbers with respect to the $Q$-Cantor series expansion for certain $Q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance","submitted_at":"2009-11-08T03:16:59Z","abstract_excerpt":"A. Renyi \\cite{Renyi} made a definition that gives one generalization of simple normality in the context of $Q$-Cantor series. Similarly, in this paper we give a definition which generalizes the notion of normality in the context of $Q$-Cantor series. We will prove a theorem that allows us to concatenate sequences of digits that have a special property to give us the digits of a $Q$-normal number for certain $Q$. We will then use this theorem to construct a Q and a real number $x$ that is $Q$-normal."},"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":"0911.1485","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-11-08T03:16:59Z","cross_cats_sorted":[],"title_canon_sha256":"31eb3242b4e765740a3b7ef8356ad5add5ff60f0b754db185029b16f57582ccd","abstract_canon_sha256":"951a4e3d2cfb4a7beff66c426750d817b2b885ba56a5f3ed6f679f4f7997c03b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:29.661296Z","signature_b64":"EXecnvUaj8glQQU8nNnIaP3CbGxTNr607VUM6+r4egx3xh6d9qb9U60M9ZcwLSFKnBj5gEa6yWfv/ai8J3ZLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a45f9b150c163150784cafbdcab1172900822a651391223ec418fb8e99d49c48","last_reissued_at":"2026-05-18T04:14:29.660805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:29.660805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Construction of normal numbers with respect to the $Q$-Cantor series expansion for certain $Q$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance","submitted_at":"2009-11-08T03:16:59Z","abstract_excerpt":"A. Renyi \\cite{Renyi} made a definition that gives one generalization of simple normality in the context of $Q$-Cantor series. Similarly, in this paper we give a definition which generalizes the notion of normality in the context of $Q$-Cantor series. We will prove a theorem that allows us to concatenate sequences of digits that have a special property to give us the digits of a $Q$-normal number for certain $Q$. We will then use this theorem to construct a Q and a real number $x$ that is $Q$-normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1485","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":"0911.1485","created_at":"2026-05-18T04:14:29.660880+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.1485v2","created_at":"2026-05-18T04:14:29.660880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1485","created_at":"2026-05-18T04:14:29.660880+00:00"},{"alias_kind":"pith_short_12","alias_value":"URPZWFIMCYYV","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"URPZWFIMCYYVA6CM","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"URPZWFIM","created_at":"2026-05-18T12:26:02.257875+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/URPZWFIMCYYVA6CMV664VMIXFE","json":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE.json","graph_json":"https://pith.science/api/pith-number/URPZWFIMCYYVA6CMV664VMIXFE/graph.json","events_json":"https://pith.science/api/pith-number/URPZWFIMCYYVA6CMV664VMIXFE/events.json","paper":"https://pith.science/paper/URPZWFIM"},"agent_actions":{"view_html":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE","download_json":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE.json","view_paper":"https://pith.science/paper/URPZWFIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.1485&json=true","fetch_graph":"https://pith.science/api/pith-number/URPZWFIMCYYVA6CMV664VMIXFE/graph.json","fetch_events":"https://pith.science/api/pith-number/URPZWFIMCYYVA6CMV664VMIXFE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE/action/storage_attestation","attest_author":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE/action/author_attestation","sign_citation":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE/action/citation_signature","submit_replication":"https://pith.science/pith/URPZWFIMCYYVA6CMV664VMIXFE/action/replication_record"}},"created_at":"2026-05-18T04:14:29.660880+00:00","updated_at":"2026-05-18T04:14:29.660880+00:00"}