Schrödinger Dynamics as the Low-Spectrum Limit of SU(N)-Covariant Time–Scalar Spectral Geometry

We derive the nonrelativistic Schrödinger dynamics as the controlled low-spectrum limit of the SU(N)-covariant Time–Scalar Field Theory (TSFT) scale-chain framework. Starting from the previously established Dirac-form generator whose square yields the quadratic TSFT operator, we isolate the positive-energy branch and perform a uniform low-spectrum expansion. After removal of the fast rest-phase oscillation, the reduced evolution is shown to obey a Schrödinger type equation generated by an explicit effective Hamiltonian Heff = P2s / 2Meff, with computable lattice corrections expressed in terms of the TSFT Laplacian operator. The result is purely operator-theoretic and introduces no external quantum postulates. This completes the intrinsic kinematic bridge from TSFT spectral geometry to nonrelativistic quantum evolution.