Canonical Boundary Smoothing and Trace-Norm Cutoff Removal for the Exact Kerr--Newman APS Collar

This preprint proves a canonical boundary-smoothing mechanism for the exact stationary Kerr--Newman APS collar constructed in Paper C and connects it with the dyadic trace-norm cutoff-removal framework of Paper B. The paper studies the exact compact APS collar associated with the intrinsic spin-Dirac reduction of the stationary subextremal Kerr--Newman inner-horizon model. It identifies several natural boundary pseudodifferential mechanisms whose dyadic high-frequency contributions are trace-norm summable. These include APS commutators, the Calderón--APS defect, spectral powers, resolvent powers, and heat operators. The main theorem proves that the resulting boundary smoothing operators provide the dyadic trace-damping input required by Paper B. Consequently, the finite dyadic shell cutoffs converge in trace norm, the cutoff tail has quantitative decay, and traces against bounded test families converge uniformly in the compact collar model. This paper is Paper D in the compact-collar Kerr--Newman series. Paper A proves the APS/Fredholm and index-stability theorem on compact collars. Paper B proves dyadic shell trace-norm cutoff removal under explicit shell-damping hypotheses. Paper C constructs the exact stationary Kerr--Newman-to-APS-collar bridge. The present Paper D supplies the canonical boundary smoothing mechanism that feeds the Paper B trace-class theorem on the exact collar produced in Paper C. The scope is local, elliptic, and boundary-spectral. The paper does not claim full nonlinear Einstein--Maxwell evolution, nonlinear stability of the Cauchy horizon, mass-inflation control, black-hole evaporation, Page curve behavior, observational comparison, or a complete black-hole information theorem.