Constructive Fourier realization

Equation (eq:finite-weyl) is a proved finite translation–character comparison. It is not the source's central-torsor/transgression theorem.

On a single charge sector, $Z_a$ is a scalar. Consequently its conjugation action on a density matrix is identity. Density-matrix tomography alone cannot verify that scalar phase. The linear identity $F_d{S}_a=Z_a{F}_d$ has been checked algebraically, rather than inferred from channel tomography.