{"paper":{"title":"An explicit upper bound for the Helfgott delta in SL(2,p)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Colva Roney-Dougal, Jack Button","submitted_at":"2014-01-13T15:11:19Z","abstract_excerpt":"Helfgott proved that there exists a $\\delta>0$ such that if $S$ is a symmetric generating subset of $SL(2,p)$ containing 1 then either $S^3=SL(2,p)$ or $|S^3|\\geq |S|^{1+\\delta}$. It is known that $\\delta\\geq 1/3024$. Here we show that $\\delta\\leq(\\log_2(7)-1)/6 \\approx 0.3012$ and we present evidence suggesting that this might be the true value of $\\delta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2863","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}