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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 $\\delta$."},"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":"1401.2863","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-01-13T15:11:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"95109e873663415220223de2417b18c138d40c3b19baecfcef97630684620a92","abstract_canon_sha256":"00e316680273e4e81c9bee6cce8fe2a8ffa4da697d763355597fa5b172b25042"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:07.758699Z","signature_b64":"HX8jchHEP3bPEx6ndK+ngPhmGr4actX5+4oyo55dYZUoo76GwtY/hdxFjqrw3C800aWDpjYlMWIJsR48MZk6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"421e48dc0fa8146b6e32bf87fd1dc710ff73fe427a04cfe12efa3e946f26c6ed","last_reissued_at":"2026-05-18T02:33:07.758232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:07.758232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $|S^3|\\geq |S|^{1+\\delta}$. 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