{"paper":{"title":"Polynomials nonnegative on the cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer, Sebastian Wenzel","submitted_at":"2016-07-29T07:06:24Z","abstract_excerpt":"In 2010, Marshall settled the strip conjecture, according to which every polynomial in $\\mathbb{R}[x,y]$, nonnegative on the strip $[-1,1]\\times\\mathbb{R}$, is a sum of squares and of squares times $1-x^2$. We consider affine nonsingular curves $C$ over $\\mathbb{R}$ with $C(\\mathbb{R})$ compact, and study the question whether every $f$ in $\\mathbb{R}[C][y]$, nonnegative on $C(\\mathbb{R})\\times\\mathbb{R}$, is a sum of squares in $\\mathbb{R}[C][y]$. We give an affirmative answer under the condition that $f$ has only finitely many zeros in $C(\\mathbb{R})\\times\\mathbb{R}$. For $C$ the circle $x_1^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08705","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}