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Also, from the Bourgain-Milman bound on the volume ratio of Banach spaces in terms of their cotype $2$ constant, we obtain information on the cotype of these $3$-fold proj"},"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":"1608.08436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-30T13:08:32Z","cross_cats_sorted":[],"title_canon_sha256":"634fb25200df277bd4b13463e20fd1f05bd4c91fe391a7c5d5694c96b106e8e3","abstract_canon_sha256":"5e34918560549b28c8e6f7460f2f2b4704b7c69cbcafe32d7add0bd86f8059dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:18.115127Z","signature_b64":"iJ4aUzuTiTwI6HXY7rGfEio8cbkxT0RFHoIZOIIFzxsB/EG6wFFnd7cWY1lmFLB68WHDzgfHlzk9fqVexh9uDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ba2e620b51c94342484bb0c1136c488dbdfa64a14f63315761a1ec392990653","last_reissued_at":"2026-05-18T01:07:18.114552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:18.114552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the geometry of projective tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carsten Sch\\\"utt, Elisabeth Werner, Joscha Prochno, Nicole Tomczak-Jaegermann, Ohad Giladi","submitted_at":"2016-08-30T13:08:32Z","abstract_excerpt":"In this work, we study the volume ratio of the projective tensor products $\\ell^n_p\\otimes_{\\pi}\\ell_q^n\\otimes_{\\pi}\\ell_r^n$ with $1\\leq p\\leq q \\leq r \\leq \\infty$. 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