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In the later case, we establish a bound of the form $\\left\\Vert S f\\right\\Vert_{L^2(K)}\\geq C(I,K)|\\left\\langle f\\right\\rangle_I|$ where $\\left\\langle f\\right\\rangle_I$ is th"},"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":"1605.05511","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-18T10:47:24Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1db996a3caf58ad2e75b010f689b13efa57fa69a2da3e27f04ac47c6306b3a1b","abstract_canon_sha256":"86ee4d5d7e26cfa21cde5b14fd9105244a4f0d89f7fdfb045a2b1744c4a97201"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:31.059573Z","signature_b64":"SCVrpW3EgSt4OLCJ+7ywcFsBPmLQkS6fVb1R84SP0xT8bOU8Z64O2u/ZJltGBvJF78DOuazabBnvm4EDNxEKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c1d87d6048e092248df7bb290152b1f131f43380dd846a7f71962711b7bf107","last_reissued_at":"2026-05-18T00:56:31.058692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:31.058692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower bounds for the dyadic Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Brett D. 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