Volume-uniform local density bounds and seven exact temporal decimations in an SU(3) lattice transfer model
Year: 2026
Type: preprint
Abstract: We study an SU(3) lattice transfer model on three-dimensional open spatial boxes with discrete time, a spatial plaquette interaction, and a correction coupling plaquettes on adjacent time slices. For |bs| ≤ 1/250000 and 0 ≤ η ≤ 1/480000, we prove that the two-time, eight-link marginal of a plaquette has logarithmic density oscillation less than 0.01 relative to the corresponding independent-chain reference after each of seven exact dyadic temporal decimations. The bounds are uniform in spatial volume and include every generated interaction order. A localization lemma transfers interaction estimates to the marginal density, while a connected expansion and complex-disc estimates control the complete higher-order remainder. At temporal width 128, a character decomposition of the internal first-order response reduces the full density bound to less than 0.0036. Its supremum B128 is enclosed in a rational interval of width less than 2.392 × 10−41. We also prove uniform convergence of the centered response to an explicit sum of endpoint functions. The density estimate passes to local weak limits without loss of its constant. Positive transfer and retained-source spectral scales are preserved by exact temporal projection. We identify the finite-step contribution to the Spectral Chaos G1–G4 programme and the additional estimates needed for spatial coarse-graining and a continuum limit. Arithmetic certificates and reproduction code accompany the paper.
Author: Umeno, Ken
Institution: Kyoto University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225777036
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