An all-order invariant domain for exact temporal decimation in an SU(3) lattice transfer model

We construct an invariant domain for exact temporal decimation of symmetric kernels with general two-layer spatial interactions. A canonical Haar decomposition separates a scalar, a one-time endpoint potential and a remainder joining the two retained times. In a spatially weighted Wiener norm, the domain B + 3ε ≤ a/16 is preserved by exact kernel squaring, with B′ ≤ B + 2ε and ε′ ≤ 12ε2/a. The support weights and the common analytic radius are unchanged. For an SU(3) lattice transfer model with |bs| ≤ 1/250000 and 0 ≤ η ≤ 1/480000, rational certificates verify entry at temporal width 128 with a = 0.1, spatial tree weight 0.01 and analytic radius 2. All subsequent dyadic temporal decimations are therefore controlled without truncating generated interactions. We obtain a local endpoint limit, the finite-volume spectral pressure, and a volume-uniform lower bound mlatt > 0.01190 for all finite-volume non-Perron modes of this fixed lattice model. The second- and third-order boundary estimates needed for entry are proved in an appendix. We distinguish these results from spatial renormalization and a continuum limit, and formulate four precise requirements for a subsequent connection to spatial coarse-graining with sources and large-field control.