{"paper":{"title":"Asymptotic contractivity of the Bohnenblust--Hille inequality for polynomials with few interacting variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel N\\'u\\~nez Alarc\\'on, Diana Marcela Serrano Rodr\\'iguez, Jorge Nicol\\'as Caro Montoya","submitted_at":"2026-07-23T02:19:14Z","abstract_excerpt":"Let $K_{m,M}$ denote the optimal Bohnenblust--Hille constant on the class of $m$-homogeneous polynomials all of whose monomials involve at most $M$ different variables. We prove that, for every fixed $M$, these constants are asymptotically contractive: \\[ \\lim_{m\\to\\infty}K_{m,M}=1. \\] More precisely, \\[ 1\\le K_{m,M}\\le A_M^{M/m}m^{(M^2-1)/(2m)}, \\] where $A_M$ depends only on $M$. The argument combines bounded projections onto exact support levels, a random colouring of the active variables, the classical multilinear Bohnenblust--Hille inequality and interpolation with Parseval's identity. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20847","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.20847/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}