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This was previously unknown even for simple properties such as cubic polynomials over $\\mathbb{F}_2$.\n  Our test is simple: take a restriction of $f$ to a constant dimensional affine subspace, and measure its distance from $\\cal{P}$. We show that by choosing the dimension large enough, this approximates with"},"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":"1306.0649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-06-04T04:10:08Z","cross_cats_sorted":[],"title_canon_sha256":"99a7cf27b2a755a27fd073dd9b3b12febd4e946a81d763f5ad083bf9dd6649f3","abstract_canon_sha256":"36b56ebd93492c7d97ce056ef547b799b23c01f43e6efc85d7633b7f22fb99af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:54.464372Z","signature_b64":"v5GxhQ+jA4T1No0IQtD6TpchQS6u+k6EnvjE9coP1JulQtA6eE6X9iJuzbN8BUo6Lyg8AFtHMLuZTCrHadSIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"034d7ad6ddc190b8262e496f4e1e54265f0303b56872ca1c92faae49e3466474","last_reissued_at":"2026-05-18T03:21:54.463643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:54.463643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating the distance from testable affine-invariant properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Hamed Hatami, Shachar Lovett","submitted_at":"2013-06-04T04:10:08Z","abstract_excerpt":"Let $\\cal{P}$ be an affine invariant property of functions $\\mathbb{F}_p^n \\to [R]$ for fixed $p$ and $R$. 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