{"id":"hexagon/2611.00015","pdf":"https://hexagonmath.org/pdf/2611.00015v1","url":"https://hexagonmath.org/abs/2611.00015v1","tags":["math.RT","msc:13F60","msc:14M25","Cluster Algebra"],"score":0,"title":"Positive polytopes and the full Fock–Goncharov conjecture","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.CO","summary":"We prove the origin-interior form of the polytope criterion of Gross, Hacking, Keel and Kontsevich: over a field of characteristic zero, full Fock–Goncharov for a principal coefficient cluster variety is equivalent to the existence of a bounded full-dimensional positive polytope containing the origin in its interior. Replacing the interior condition by membership of the origin gives a false criterion.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}