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Our first main result asserts that for $q_{1},...,q_{m}>0$ and an infinite-dimensional Banach space $Y$ attaining its cotype $\\cot Y$, if \\begin{equation*} \\frac{1}{p_{1}}+...+\\frac{1}{p_{m}}<\\frac{1}{\\cot Y}, \\end{equation*} then the following assertion"},"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":"1602.00178","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-01-31T00:39:32Z","cross_cats_sorted":[],"title_canon_sha256":"be3d5c03bd1f926e711cbeaead3d1353f618bed89e2c14356c0dded4657996dc","abstract_canon_sha256":"55871d5881d05e368643d2e4680117ca3deb3ea95a81e7981c4e43e2c1d73f70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:30.950194Z","signature_b64":"9YaStJ6Iqt0tqwCLXZD190K32s07/jzCmTryLB66uw+mtfXQjUGJKU5HhjCKZUEPSoiWhEwvecSldkSwJSlEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46fd84ae7407510aa1ba13d4d6b2ba540bb71201c378693de20ddc35ad3e240b","last_reissued_at":"2026-05-18T00:10:30.949641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:30.949641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal exponents for Hardy--Littlewood inequalities for $m$-linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"D. 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