{"id":"hexagon/2611.00122","pdf":"https://hexagonmath.org/pdf/2611.00122v1","url":"https://hexagonmath.org/abs/2611.00122v1","tags":["math.CO","math.QA","msc:18A32","msc:18M05","msc:05C20","acyclic categories","causal networks","convex minors","gauge groupoids","homotopy descent"],"score":0,"title":"Acyclic Networks: Causal Comparisons, Convex Minors, and Gauge Descent","domain":"math.CT","source":"hexagon","authors":["Zhenyu Sun"],"reviews":0,"subject":"math.CT","summary":"We study natural transformations, minors, and symmetric monoidal decorations of finite directed acyclic networks. For any weakly connected small source category, a natural transformation into a free acyclic path category is determined by one component. If more than one transformation exists, common prefixes and suffixes give a canonical factorization through two constant functors and identify the transformation set with a single set of directed paths. Consequences include boundary rigidity, a decision algorithm, and a fundamental-group obstruction to non-uniqueness. For fusion–embedding…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-05","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}