{"id":"hexagon/2610.00645","pdf":"https://hexagonmath.org/pdf/2610.00645v1","url":"https://hexagonmath.org/abs/2610.00645v1","tags":["math.RT","msc:13F60","msc:05A15","msc:13F25","Cluster Algebra"],"score":0,"title":"Algebraicity of rank-two scattering wall functions","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Qiyue Tang"],"reviews":0,"subject":"math.CO","summary":"We prove that every wall function in the rank-two scattering factorization determined by two polynomial initial walls over a field of characteristic zero is algebraic. This resolves the algebraicity question posed by Kontsevich and recorded by Gross and Pandharipande, and its cluster-scattering formulation in the work of Burcroff, Lee, Mou, Musiker, and Reineke.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}