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It is a well-known fact that there is a subspace $V \\leq \\mathbb{F}^n$, $\\mbox{codim} V \\ll_{\\delta} 1$, and an $x$, such that $A$ is $\\delta$-uniform when restricted to $x + V$ (that is, all non-trivial Fourier coefficients of $A$ restricted to $x + V$ have magnitude at most $\\delta$). We show that if $\\mathbb{F} = \\mathbb{F}_2$ then it is possible to take $x = 0$; that is, $A$ is $\\delta$-uniform on a subspace $V \\leq \\mathbb{F}^n$. We give an example to show that this is not necessarily possible when $\\mathbb{F} = \\"},"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":"1510.08739","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-29T15:28:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d48525fe960f8e6a5f937ba8d9182ee1350c76df9f3fe701faa09dc10c64c732","abstract_canon_sha256":"19700c2152815928d3d6903aeed894dba39e1957d92db4fc68feaa3f42582803"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:40.014518Z","signature_b64":"UF8oefxkA9u5EY2UNqenLj516sdJgef3HOQNOzmA8h3oAdDKMbzlNnabua//2unKozN4kaqQuNGvyTEX2p/WDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b91a4bda2b1034d5f831d37abf7662f438e32228a9aa68894149abf66df0592","last_reissued_at":"2026-05-18T01:10:40.014076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:40.014076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier uniformity on subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Ben Green, Tom Sanders","submitted_at":"2015-10-29T15:28:47Z","abstract_excerpt":"Let $\\mathbb{F}$ be a fixed finite field, and let $A \\subset \\mathbb{F}^n$. 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