Extended Technical Summary (Executive Summary): Comprehensive Verification of the Gauge Theories with Boundary Program (Stages 1–8)

This document presents a comprehensive technical and analytical review of the results of the fundamental research cycle by A. V. Turenko (2026). Within the program, the apparatus of rigorous constructive field theory, the differential geometry of Rvachev–Kravchenko R-functions, waveguide Batalin–Vilkovisky (BV-BFV) quantization, and precision numerical lattice simulations (SU(2) and SU(3) QCD) have been successfully unified. The summary details strict mathematical proofs for connected covariance exponential decay, gauge decoupling of edge modes, and the spectral mass gap under fixed regularization cutoffs. It balances these theoretical achievements with a full 3-loop renormalization group numerical verification pipeline on small lattices within Google Colab, establishing the limits of low-resource setups and laying out the complete technical specification for high-performance supercomputing (HPC) environments.