Finite-Window Energy and Spectral Conservation

Establish energy and spectral conservation laws under finite-window measurement. Core result: for windowed readout with window w and spectral density \rho, windowed energy E_w=\int Ew(E)\rho(E)dE satisfies: (i) Conservation: under unitary evolution \partial_tE_w=0 when w time-independent; (ii) Covariance: gauge-invariant under phase transformations; (iii) NPE closure: discrete approximation with alias+EM+tail error decomposition.