{"id":"hexagon/2610.00567","pdf":"https://hexagonmath.org/pdf/2610.00567v1","url":"https://hexagonmath.org/abs/2610.00567v1","tags":["math.FA","msc:46L07","operator systems; lifting property; nuclearity; weak expectation property"],"score":0,"title":"The regular pentagonal system and the Smith--Ward problem","domain":"math.OA","origin":"ai-generated","source":"hexagon","authors":["Shengwei Qiu","Thomas Sinclair"],"reviews":0,"subject":"math.OA","summary":"The three-dimensional function system of the regular pentagon fails the lifting property, giving a counterexample to the operator-system formulation of the Smith--Ward problem with C$^*$-envelope $\\mathbb C^5$. We construct unital $k$-positive maps from this fixed system into matrix algebras where distance from every ucp map is bounded below independently of $k$. We also prove that every regular polygon system with at least five vertices detects nuclearity, while its dual characterizes the weak expectation property. These tensor-product characterizations follow from a graph dichotomy: a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}