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We study the asymptotic geometric mean errors $e_{n,0}(\\mu),n\\geq 1$, in the quantization for the in-homogeneous self-similar measure $\\mu$ associated with the condensation system $((f_i)_{i=1}^N,(p_i)_{i=0}^N,\\nu)$. We focus on the following two independent cases: (I) $\\nu$ is a self-similar measure on $\\mathbb{R}^q$ associated with $(f_i)_{i=1}^N$; (II) $\\nu$ is a self-similar measure associated with"},"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":"1411.3359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-10-23T06:54:52Z","cross_cats_sorted":["cs.IT","math.FA","math.IT"],"title_canon_sha256":"fc43fa68034d980d674798ea5f4f78ed340fbde9f1351399ee9828cd3043b734","abstract_canon_sha256":"14c1f92bf2615d3e4cbb281f1155278e524be6872c103542f529938e1c40f700"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:43.981770Z","signature_b64":"gGTxkqouolpNvdbjkQVrS648q5+3mbQJcshepsrrjYlWnWwWVNWN5etHX/xwBKhC1h3UZArCriAohA62wmDRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b963b5255eda7eea6f63eb012fe99be5aa3d95eca276f029840eb93548780f5f","last_reissued_at":"2026-05-18T02:37:43.981304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:43.981304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the geometric mean error for in-homogeneous self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"math.DS","authors_text":"Sanguo Zhu, Yongjian Sheng, Youming Zhou","submitted_at":"2014-10-23T06:54:52Z","abstract_excerpt":"Let $(f_i)_{i=1}^N$ be a family of contractive similitudes on $\\mathbb{R}^q$ satisfying the open set condition. 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