Error Controllability Under Finite-Order Discipline: PSWF/DPSS Extremal Windows Uniqueness, Integer Leading Terms (Spectral Flow/Index of Projection Pairs), and $10^{-3

Under unified Fourier normalization \widehat f(\xi)=\int_{\mathbb R}f(t)e^{-2\pi i t\xi}\,dt (frequency in cycles), we construct error discipline around time-limiting--band-limiting concatenated operators: windowing main leakage, multiplicative cross-terms, and ``sum--integral difference'' are organized into computable chains of ``topological integer leading terms + analytic tail terms.'' On the continuous side, K_c=D_TB_\Omega D_T (discrete side K_{N,W}=T_NB_WT_N) yields uniqueness of extremal