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Lafer asked for a construction of a $Q$-distribution normal number for an arbitrary $Q$. Under a mild condition on $Q$, we construct a set $\\Theta_Q$ of $Q$-distribution normal numbers. This set is perfect and nowhere dense. Additionally, given any $\\alpha$ in $[0,1]$, we provide an explicit example of a sequence $Q$ such that the Hausdor"},"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":"1010.2782","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-10-13T21:52:31Z","cross_cats_sorted":[],"title_canon_sha256":"c8440e404cf1d5278a96f4fecea273c4b79046992afcf08bcfa6f386d44fc42f","abstract_canon_sha256":"09d354d0826a0535df6097e9a94d1caa1056c3a23bacccce49fd23181392610a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:48.803076Z","signature_b64":"tHnXVHmUM5JimJWBu2SiWXWlicpBwf9GqZIwx9L+6iVj2/CnP3kgt0PvRTrFIbinjbPyOVS7O1ns5SLQXRaMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d45955961a8b3f15fef86fca14ea5b2208748cec36cc90a11fb1faec79a17eb","last_reissued_at":"2026-05-18T02:55:48.802544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:48.802544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cantor series constructions of sets of normal numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance","submitted_at":"2010-10-13T21:52:31Z","abstract_excerpt":"Let $Q=(q_n)_{n=1}^{\\infty}$ be a sequence of integers greater than or equal to 2. 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