{"paper":{"title":"A Positivstellensatz for forms on the positive orthant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer, Colin Tan","submitted_at":"2017-01-06T09:40:12Z","abstract_excerpt":"Let $p$ be a nonconstant form in $\\mathbb{R}[x_1,\\dots,x_n]$ with $p(1,\\dots,1)>0$. If $p^m$ has strictly positive coefficients for some integer $m\\ge1$, we show that $p^m$ has strictly positive coefficients for all sufficiently large $m$. More generally, for any such $p$, and any form $q$ that is strictly positive on $(\\mathbb{R}_+)^n\\setminus\\{0\\}$, we show that the form $p^mq$ has strictly positive coefficients for all sufficiently large $m$. This result can be considered as a strict Positivstellensatz for forms relative to $(\\mathbb{R}_+)^n\\setminus\\{0\\}$. We give two proofs, one based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01585","kind":"arxiv","version":3},"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"}