CDUFD Supplementary Material III: Critical Emergence of Gauge Fields– Heuristic Exploration and Conceptual Analysis

This is the third supplementary material of the CDUFD qualitative framework. For the U (1) gauge field we give a formal derivation (Stückelberg mechanism) from the U (1) ₁-₋ subgroup of SO (8). For the SO (8) Yang–Mills field we only provide a heuristic exploration. A rigorous derivation from a four‑dimensional non‑linear sigma model to Yang–Mills theory does not exist; the known construction works in two dimensions only. Therefore the SO (8) gauge group is taken as an A5‑anchored input, and its critical emergence is listed as an open problem. All open problems are explicitly identified. The U (1) part yields the scaling law 1/g'² ^2.