Operator Package 2: Discretized Log-Scale Spectral Mechanics for APM Boundary Closure

This paper standardizes Operator Package 2: an APM-ready discretization layer that converts the continuous log-scale backbone of Operator Package 1 into a controlled, self-adjoint, finite-window module with discrete mode families. The organizing principle is that physical APM systems occupy a finite scale window and that Aether-unit packing/holonomy induces boundary closure. Finite QMU-normalized scale window. The log-scale coordinate is taken as$$q=\log(\ell/\lambda_C),\qquad q\in[q_-,q_+],$$with window length$$L_q=q_+-q_-=\log(\ell_{\max}/\ell_{\min}).$$ Ledger-One normalization anchor. The module is ledger-anchored through the standardized closure$$A_u\cdot \mathrm{curl}={F_q}^{2}{\lambda_C}^{2}.$$Define…