We establish a rigorous Bohr-type quantization mechanism within the SU (N) -covariant Time–Scalar Field Theory (TSFT) scale-chain framework. Building on the previously constructed self-adjoint covariant operator and its holonomy-controlled Floquet sectorization, we prove that imposition of boundary or half-line compatibility conditions converts the continuous Floquet family into a discrete admissible spectrum. The selection mechanism is governed by the phase–amplitude monodromy operatorM = (ϕ^−L/2) W, where W is the unit-cell holonomy and ϕ > 1 is the TSFT drift parameter. Using transfer-matrix analysis and a Liouville stretching argument, we derive an explicit asymptotic quantization law λn ∼ (nπ/S) ², thereby recovering a Bohr-type discrete hierarchy without invoking particle-model assumptions. Holonomy controls fine-structure splitting, while drift determines the principal exponential hierarchy.
Jordan Gabriel Farrell (Sun,) studied this question.