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The exact values of the constants $K_{n}$ are still waiting to be discovered since eighty years ago; recently, it was proved that $(K_{n})_{n=1}^{\\infty}$ has a subexponential growth. In this note we go a step further and address the following question: Is it true that \\[ \\lim_{n\\rightarrow\\infty}(K_{n}-K_{n-1}) =0? \\] Our main result is a Dichotomy Theorem for the constants satisfying the Bohnenblust--Hille inequality; in particular we show that the answer to the a"},"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":"1205.2385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-05-10T20:31:32Z","cross_cats_sorted":[],"title_canon_sha256":"43a5b0c025ee9224ba3d78783a479b2fff309963703cebcdbf7f74bb9932db31","abstract_canon_sha256":"973e83846a442e1f264915f4f99f67646e30d6782d046ba5c0b18570a18a105d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:55.681158Z","signature_b64":"JvXD84LZP6gFyO2VJf0i67knAyvCZ1c6Nw62P+om7BDFwS1A4DH0wwfkxLF2FBz9f8DXjLeXYkqPKB2/k7YmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bff57df5ef9ce86fd436f46ddc1308b01046d5b3a1fac216fef5dac2ffefb381","last_reissued_at":"2026-05-18T03:55:55.680637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:55.680637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the growth of the optimal constants of the multilinear Bohnenblust--Hille inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Nu\\~nez-Alarc\\'on, Daniel Pellegrino","submitted_at":"2012-05-10T20:31:32Z","abstract_excerpt":"Let $(K_{n})_{n=1}^{\\infty}$ be the optimal constants satisfying the multilinear (real or complex) Bohnenblust--Hille inequality. 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