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Let $\\mu$ be the infinite product measure (Moran measure) on $E$ associated with a sequence $(\\mathcal{P}_k)_{k\\geq1}$ of positive probability vectors with $\\mathcal{P}_k=(p_{k,j})_{j=1}^{n_k},k\\geq 1$. We assume that \\[ \\inf_{k\\geq1}\\min_{1\\leq j\\leq n_k}c_{k,j}>0,\\;\\inf_{k\\geq1}\\min_{1\\leq j\\leq n_k}p_{k,j}>0. \\] For every $n\\geq 1$, let $\\alpha_n$ be an $n$ optimal set in the quantization for $\\mu$ of order $r\\in(0,\\infty"},"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":"1802.03723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-11T11:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"e242805576c74955e379a215b82a283a5d600f3fbd6fd9f47253c4610d041d1a","abstract_canon_sha256":"56d0fef2f4355369d47ebf93c73451752c18e93c57cab07bf81a36822a5aa4f1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:50.649989Z","signature_b64":"6rGwQZN0AH1QQHBMYYPRo4qbnNosVI3+bQcpyfpC+25N1Kc0CT81qbdSYlW75YzATZxCC5f98dt9cxgDvk/sAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6c799fdbcaf8a6a64c5f00a3b05a32f2a68d30bfdb60ea5a09615a6463042df","last_reissued_at":"2026-05-18T00:23:50.649408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:50.649408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic uniformity of the quantization error for Moran measures on $\\mathbb{R}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sanguo Zhu","submitted_at":"2018-02-11T11:18:58Z","abstract_excerpt":"Let $E$ be a Moran set on $\\mathbb{R}^1$ associated with a closed interval $J$ and two sequences $(n_k)_{k=1}^\\infty$ and $(\\mathcal{C}_k=(c_{k,j})_{j=1}^{n_k})_{k\\geq1}$. 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