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We show the following applications of our bounds. Let $[\\mathbb{Z}/N\\mathbb{Z}]_p$ be the random subset of $\\mathbb{Z}/N\\mathbb{Z}$ containing each element independently with probability $p$.\n"},"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":"1711.05624","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-15T15:29:16Z","cross_cats_sorted":["cs.DM","math.FA","math.PR"],"title_canon_sha256":"936f405202471c16d40a6416f003b35833aecece896c498dbdd6c6e6d3e17a7f","abstract_canon_sha256":"1f42727cee78613af88e276f739edd5ea8c16e9b24e956799a400a80d0cb55a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:49.717293Z","signature_b64":"usiKy/JY80YZJPXxPWE29sdZzYtMhxMGWP+O6GcJST4Hsugk9U03M3nVG4Oj5aRPniSTcufcT5nAX3iSyGQFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15410808a12008e98ac0aa9662e5296fa256cdacda5197a95001d923bd4536a3","last_reissued_at":"2026-05-18T00:02:49.716852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:49.716852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian width bounds with applications to arithmetic progressions in random settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.FA","math.PR"],"primary_cat":"math.CO","authors_text":"Jop Bri\\\"et, Sivakanth Gopi","submitted_at":"2017-11-15T15:29:16Z","abstract_excerpt":"Motivated by problems on random differences in Szemer\\'{e}di's theorem and on large deviations for arithmetic progressions in random sets, we prove upper bounds on the Gaussian width of point sets that are formed by the image of the $n$-dimensional Boolean hypercube under a mapping $\\psi:\\mathbb{R}^n\\to\\mathbb{R}^k$, where each coordinate is a constant-degree multilinear polynomial with 0-1 coefficients. We show the following applications of our bounds. 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