Explicit Hilbert-Schmidt Control of the Four-Dimensional Wilson SU(2) Armillary Tensor

Abstract

We study the exact reduced armillary tensor representation of four-dimensionalWilson SU(2) lattice gauge theory in the strong-coupling regime and derive anexplicit Hilbert-Schmidt majorant for the normalized site tensor. Two logicallyindependent sufficient-condition results are presented. First, a deliberatelyconservative quantitative estimate places the Wilson tensor inside thetruncation-free four-dimensional rearrangement-RG basin for beta < 10^-18700.Second, bypassing the rearrangement map entirely, an exact-rational directpolymer certificate gives the weighted Kotecky-Preiss condition forbeta <= 2.7 x 10^-6, leading to fixed-lattice exponential clustering and atransfer-matrix spectral-gap corollary under the standard cited structuralinputs. The two results are explicitly separated. No continuum beta -> infinity,a -> 0 result is claimed, and this work does not solve the Yang-Mills Millenniumproblem. Strong-coupling lattice mass gaps are not claimed as novel; themodel-specific contribution is the explicit four-dimensional Wilson SU(2)armillary-to-Hilbert-Schmidt control and its connection to the rigorousfour-dimensional truncation-free rearrangement basin, together with theseparate direct-polymer certificate.