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Let $\\vec{x}$ be a set of $n$ differential variables, $\\vec{f}$ a finite family of differential polynomials in the ring $K\\{\\vec{x}\\}$ and $f\\in K\\{\\vec{x}\\}$ another polynomial which vanishes at every solution of the differential equation system $\\vec{f}=0$ in any differentially closed field containing $K$. Let $d:=\\max\\{\\deg(\\vec{f}), \\deg(f)\\}$ and $\\epsilon:=\\max\\{2,{\\rm{ord}}(\\vec{f}), {\\rm{ord}}(f)\\}$. We show"},"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":"1305.6298","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-05-27T19:14:14Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"fe0de114d5967357dec2319c3190432cfab8447c4b668cbf255108c3a9311487","abstract_canon_sha256":"69e42c30a1ead0b43465eb61a1b23d02ceb1fd096a3c6280c6b50943bf1a9597"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:34.925602Z","signature_b64":"UbzP21D4T1m44oswrrTLeIq3X9C5oXHgh8FvRNSWrmRvaGAwN7w6A7slFWaTg7v8L422M9sQAWLHH9W40XSWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a49ede1bf84776c623f3239232d7e86b0455a3350958936f4d84df92ca1eadce","last_reissued_at":"2026-05-18T03:02:34.925010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:34.925010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Effective Differential Nullstellensatz for Ordinary DAE Systems with Constant Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Gabriela Jeronimo, Lisi D'Alfonso, Pablo Solern\\'o","submitted_at":"2013-05-27T19:14:14Z","abstract_excerpt":"We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants $K$ of characteristic $0$. Let $\\vec{x}$ be a set of $n$ differential variables, $\\vec{f}$ a finite family of differential polynomials in the ring $K\\{\\vec{x}\\}$ and $f\\in K\\{\\vec{x}\\}$ another polynomial which vanishes at every solution of the differential equation system $\\vec{f}=0$ in any differentially closed field containing $K$. Let $d:=\\max\\{\\deg(\\vec{f}), \\deg(f)\\}$ and $\\epsilon:=\\max\\{2,{\\rm{ord}}(\\vec{f}), {\\rm{ord}}(f)\\}$. 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