DCNAB: A Gauge-Invariant Double-Cycle Diagnostic and Boundary-Contraction Framework

DCNAB is a self-contained framework for probing non-Abelian compatibility between two based gauge holonomies and for controlling the propagation of boundary information through nested lattice collars. The local observable is the normalized Frobenius norm of a matrix commutator, equivalently the real-trace defect of the group commutator. A finite-resolution Laplace discriminator compares two normalized channels without assuming a protected topological index. Exact bounds establish gauge invariance, compact range, discretization stability, and statistical estimability. In an analytically solvable Gaussian two-matrix model on su(3), the channel ordering is proved for every positive resolution parameter and its large-resolution limit is obtained from the Weyl integration formula. The global layer uses exact inward conditional boundary kernels and a separator-aware Dobrushin comparison to obtain rigorous remote-boundary forgetting under an explicit contraction certificate. The framework provides falsifiable lattice observables and conditional mathematical certificates. It does not by itself construct four-dimensional continuum Yang-Mills theory or prove a mass gap.