Holonomy and Floquet Sectorization in SU(N)-Covariant Time–Scalar Spectral Geometry

We extend the attenuated discrete scale-chain operator underlying Time–Scalar Field Theory (TSFT) to an internal symmetry setting by introducing SU(N)-covariant transport along the scale direction. The resulting operator is constructed rigorously from a nonnegative quadratic form, yielding a unique self-adjoint, nonnegative block Jacobi operator via Friedrichs extension. For periodic unit-cell data, we establish a Floquet (Bloch) direct-integral decomposition into finite-dimensional Hermitian fibers. In one dimension, all gauge-invariant spectral dependence is shown to reduce to the conjugacy class of the unit-cell holonomy W = QL r=1 Ur. We provide an explicit SU(2) band-splitting formula for L = 1 and a constructive holonomy normal form for general L. We then reintroduce TSFT fractal drift coefficients and prove (via unitary rescaling) that drift preserves holonomy sectorization while contributing only a scalar amplitude factor on the Floquet closure. Numerical checks are specified at the fiber level to verify holonomy splitting and drift scaling without invoking any particle-model identification.