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For any $\\epsilon>0$, we prove that for any polynomial $f(x)\\in\\mathbb{F}_2[x]$ with degree $n$, there exists a squarefree polynomial $g(x)\\in\\mathbb{F}_2[x]$ such that $\\mathrm{deg} (g) \\le n$ and $L_{2}(f-g)<(\\ln n)^{2\\ln(2)+\\epsilon}$ (where $L_{2}$ is a norm to be defined). As a consequence, the analogous result holds for polynomials $f(x)$ and $g(x)$ in $\\mathbb{Z}[x]$."},"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":"1906.07904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-06-19T04:05:16Z","cross_cats_sorted":[],"title_canon_sha256":"40d2858ffa54a4f8face274f0ffbdcd4e3a6afbc55fc331626ca19b991a49fa2","abstract_canon_sha256":"da62c0b59c9a3dbfa649eef3d408b1934a4115a5d4a7f6b9a7aadf94d64a3fe1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:57.348826Z","signature_b64":"Q8lW4zvQk0g+weKObYaA6I02WTveFzq2C07gOaVfhJQ5irU4gJvbD/m4yzSQY1OfKfOZweq1kFlZNYvd5DHODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efbf48c35dd2820530ec0a19555b7a3c8538471f5b75f19d157011c5650e488c","last_reissued_at":"2026-05-17T23:42:57.348172Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:57.348172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Distance to a Squarefree Polynomial Over $\\mathbb{F}_2[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Filaseta, Richard A. 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