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If there exists a measurable set $A\\subset E$ with $0<\\mathcal H_\\theta(A)<\\infty$ such that $\\mathcal H_\\theta\\lfloor_A$ is nonatomic, we prove that there is no bounded linear extension operator $\\oper"},"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":"2607.11604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-13T14:28:50Z","cross_cats_sorted":[],"title_canon_sha256":"236bfbaef25a2fa79a852c4c73fe119d3f7e6f28320fd6e0e858dffb64beb92d","abstract_canon_sha256":"8518bfab5cf008f4b521e5a0353c1cb942d0fea0ba546f4f75deb792b210ab36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T02:22:14.555733Z","signature_b64":"L7sB1BHN86UHsvzZlhJPorDZpgeuX68JAjs6G5enDdHFFFPkbxKtN0JB2wVeWgIZD1zKQKXWS1D4b9gCjcmaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0038131af227d921d13187ecba31e10ad7c04a8351900e2b8504ab6823b0e99","last_reissued_at":"2026-07-14T02:22:14.554760Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T02:22:14.554760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonexistence of Bounded Linear Extension Operators for Limiting Besov Traces on Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Aleksei Y. 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