This document serves as the Technical Companion (v2.0) to the Constructive Gauge Theory Program (CGTP). It compiles the rigorous mathematical derivations that underpin the existence of the mass gap, integrating the advanced results from Technical Articles A and B. Key updates include: (1) The explicit derivation of the BZJ prescription for magnetic bions and the Exact Cancellation Lemma for Stokes singularities (Resurgence). (2) The proof of the Matching Lemma establishing the Kotecký–Preiss convergence for the Hybrid Balaban–Brydges Renormalization Group flow. (3) The functional proof of the Positivity Lemma via the Hubbard–Stratonovich dictionary, ensuring unitarity. This supplement provides the analytical “engine room” for the theorems presented in Volumes I, II, and III.Technical Note: Regarding the non-abelian fluctuation determinant, the positivity of the effective measure is structurally guaranteed by the Exact Cancellation Lemma (Chapter 5), which ensures real bion fugacity and implies effective ferromagnetic weights.
Emiliano G. Greco (Fri,) studied this question.