{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WH2SXZAJQYXSJOSTWHB5Y2QZC5","short_pith_number":"pith:WH2SXZAJ","schema_version":"1.0","canonical_sha256":"b1f52be409862f24ba53b1c3dc6a19177358cf02ac7535f2bfd46c9cdf9c058a","source":{"kind":"arxiv","id":"1310.2379","version":3},"attestation_state":"computed","paper":{"title":"Number theoretic applications of a class of Cantor series fractal functions, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Brian Li","submitted_at":"2013-10-09T07:28:10Z","abstract_excerpt":"It is well known that all numbers that are normal of order $k$ in base $b$ are also normal of all orders less than $k$. Another basic fact is that every real number is normal in base $b$ if and only if it is simply normal in base $b^k$ for all $k$. This may be interpreted to mean that a number is normal in base $b$ if and only if all blocks of digits occur with the desired relative frequency along every infinite arithmetic progression. We reinterpret these theorems for the $Q$-Cantor series expansions and show that they are no longer true in a particularly strong way. The main theoretical resu"},"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":"1310.2379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-09T07:28:10Z","cross_cats_sorted":[],"title_canon_sha256":"888871c4fa450f9a66b2d653e559e13dae35395caca40e04e1e148314530ed59","abstract_canon_sha256":"5038505e40bf6612302300ea712ac43e91b2a923088a32ae6d439482dc95d58d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:07.726134Z","signature_b64":"yTXxcWkUWRqFQ/Yair1C9KNmMDCx5QQuAiYgpVvAP16B0LFhbOtizXZXojO0lUVbIsMi9Awy9GfNeD16ZNy6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1f52be409862f24ba53b1c3dc6a19177358cf02ac7535f2bfd46c9cdf9c058a","last_reissued_at":"2026-05-18T02:47:07.725688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:07.725688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Number theoretic applications of a class of Cantor series fractal functions, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Brian Li","submitted_at":"2013-10-09T07:28:10Z","abstract_excerpt":"It is well known that all numbers that are normal of order $k$ in base $b$ are also normal of all orders less than $k$. Another basic fact is that every real number is normal in base $b$ if and only if it is simply normal in base $b^k$ for all $k$. This may be interpreted to mean that a number is normal in base $b$ if and only if all blocks of digits occur with the desired relative frequency along every infinite arithmetic progression. We reinterpret these theorems for the $Q$-Cantor series expansions and show that they are no longer true in a particularly strong way. The main theoretical resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2379","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":"1310.2379","created_at":"2026-05-18T02:47:07.725756+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2379v3","created_at":"2026-05-18T02:47:07.725756+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2379","created_at":"2026-05-18T02:47:07.725756+00:00"},{"alias_kind":"pith_short_12","alias_value":"WH2SXZAJQYXS","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WH2SXZAJQYXSJOST","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WH2SXZAJ","created_at":"2026-05-18T12:28:04.890932+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/WH2SXZAJQYXSJOSTWHB5Y2QZC5","json":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5.json","graph_json":"https://pith.science/api/pith-number/WH2SXZAJQYXSJOSTWHB5Y2QZC5/graph.json","events_json":"https://pith.science/api/pith-number/WH2SXZAJQYXSJOSTWHB5Y2QZC5/events.json","paper":"https://pith.science/paper/WH2SXZAJ"},"agent_actions":{"view_html":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5","download_json":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5.json","view_paper":"https://pith.science/paper/WH2SXZAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2379&json=true","fetch_graph":"https://pith.science/api/pith-number/WH2SXZAJQYXSJOSTWHB5Y2QZC5/graph.json","fetch_events":"https://pith.science/api/pith-number/WH2SXZAJQYXSJOSTWHB5Y2QZC5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5/action/storage_attestation","attest_author":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5/action/author_attestation","sign_citation":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5/action/citation_signature","submit_replication":"https://pith.science/pith/WH2SXZAJQYXSJOSTWHB5Y2QZC5/action/replication_record"}},"created_at":"2026-05-18T02:47:07.725756+00:00","updated_at":"2026-05-18T02:47:07.725756+00:00"}