Heisenberg-Type Uncertainty from Scale–Translation Weyl Pairs in SU(N)-Covariant Time–Scalar Spectral Geometry

We establish a Heisenberg-type uncertainty structure intrinsic to the SU (N) -covariant Time–Scalar Field Theory (TSFT) scale-chain framework. Building on prior work that constructed the covariant operator, demonstrated holonomy-controlled Floquet sectorization, and derived Bohrtype discretization via monodromy closure, we identify the canonical conjugate pair generated by discrete scale translation. Working on the cell Hilbert space ℓ² (Z;CNL), we prove that the scale-position operator and the unitary scale-translation operator satisfy an exact Weyl commutation relation. Under the Floquet transform, this pair is shown to be unitarily equivalent to the differential–multiplication duality (i∂κ, ; e^−iκ), where the closure phase κ is the spectral variable governing TSFT monodromy. From this Weyl structure we derive a rigorous scale–phase uncertainty bound, demonstrating that strong localization along the TSFT scale chain necessarily induces delocalization in closure phase. This provides the Heisenberg-type complement to the previously established Bohr discretization mechanism. The result completes the minimal operator-theoretic backbone of the TSFT spectral program: covariant construction, holonomy sectorization, boundary-induced quantization, and canonical conjugacy. No particle identification is asserted; the work is purely structural.