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Recently, Alman and Williams showed, contrary to common belief, that the $2^n \\times 2^n$ Hadamard matrix could not be used for Valiant's program as it is not sufficiently rigid. In this note we observe a similar `non rigidity' phenomena for any $q^n \\times q^n$ matrix $M$ of the form $M(x,y) = f(x+y)$, where $"},"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":"1708.01646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-08-04T19:23:31Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f207057198dc1f3ddb2991159e04d692fa4683c83f639f13ba7058e23ae18c31","abstract_canon_sha256":"28e5061aa79ff4111db7af41edb590f5cf97ca5adb315590f6886e7320143ffa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:35.322656Z","signature_b64":"tTAQ1Rf6J3k5qvLLmESuuCqvYbQqIGAdOHrg8kuxhrWZSURMOWtXQG/tZ2vGh/vA1FuIbqynCMkRwZqUy1P/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9192505a60976ae341dc9ab50316f02e36e90b1022aa3b7cc9eb7f5c986c8695","last_reissued_at":"2026-05-18T00:38:35.322177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:35.322177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix rigidity and the Croot-Lev-Pach lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CC","authors_text":"Benjamin Edelman, Zeev Dvir","submitted_at":"2017-08-04T19:23:31Z","abstract_excerpt":"Matrix rigidity is a notion put forth by Valiant as a means for proving arithmetic circuit lower bounds. 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