{"paper":{"title":"The open quadrant problem: A topological proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carlos Ueno, J.M. Gamboa, Jose F. Fernando","submitted_at":"2015-02-27T19:41:32Z","abstract_excerpt":"In this work we present a new polynomial map $f:=(f_1,f_2):{\\mathbb R}^2\\to{\\mathbb R}^2$ whose image is the open quadrant $\\{x>0,y>0\\}\\subset{\\mathbb R}^2$. The proof of this fact involves arguments of topological nature that avoid hard computer calculations. In addition each polynomial $f_i\\in{\\mathbb R}[{\\tt x},{\\tt y}]$ has degree $\\leq16$ and only $11$ monomials, becoming the simplest known map solving the open quadrant problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08035","kind":"arxiv","version":2},"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"}