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To elaborate more, the distance depends on whether or not $r$ and $q$ are rational powers of each other. For example, if $r^j\\neq q^m$ for all $j,m\\in \\mathbb{N},$ then $\\|B_q-B_r\\|=2,$ and if $r=q^m, m\\in \\mathbb{N},$ then $\\|B_q-B_r\\|=2(m-1)/m.$"},"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":"1708.07669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-08-25T09:53:11Z","cross_cats_sorted":[],"title_canon_sha256":"726d3cfdb95ee478af11d68acaa82bf12fb54b52622bd097c771f1d24319b60f","abstract_canon_sha256":"a9df91816eb28a9467f00819f50febe430f1083d11427420a86955b2fd1d39a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:45.772870Z","signature_b64":"cqgy+t/6dSnEopaDij7fj2iK/YkCZaDTG7XI237lZp7CYKPAK0XekPX8GTGN5XkDecxaPg8xMRaDIY+tta0WDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1aca7b1ce78b4a24edf6f89b1f83fd68abab81df1d058636cc1800314d8a51f","last_reissued_at":"2026-05-18T00:26:45.772174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:45.772174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The distance between two limit $q$-Bernstein operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mehmet Turan, Sofiya Ostrovska","submitted_at":"2017-08-25T09:53:11Z","abstract_excerpt":"For $q\\in(0,1),$ let $B_q$ denote the limit $q$-Bernstein operator. 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