USSFT Paper IV: Emergent Lorentz Symmetry and UV Constraints. How Relativistic Structure Is Recovered from the Discrete Foundation

Within the Unified Space-Time and Scale-Dependent Field Theory (USSFT) framework, Paper I (DOI: 10. 5281/zenodo. 19622931) establishes the fundamental U-field dynamics on a discrete hypercubic mesh with spacing LSRI. This lattice structure breaks continuous Lorentz invariance SO (3, 1) to the hypercubic group H₄ at the fundamental level. This paper demonstrates that full Lorentz symmetry is recovered in the infrared (IR) limit through three complementary results: (1) within the isotropized Tier-2 EFT, the stable vacuum is homogeneous and isotropic, preserving the covariant structure rather than spontaneously breaking it; (2) the light-branch dispersion relation is exactly relativistic (omega² = k² + mₚhys²), with the SRI producing only mass renormalization; (3) the leading Lorentz-violating corrections from the discrete substrate scale quadratically as (E/ESRI) ², evading the tightest linear constraints from gamma-ray burst observations by many orders of magnitude. We clarify why the U-field is not a return to luminiferous aether: particles are U-field configurations, not objects moving through a medium. Status: (B) derived emergent symmetry result under stated EFT assumptions, with (B) phenomenological constraints on Tier-1 corrections. This is Paper IV in the 18-paper USSFT technical series; for a conceptual overview, see Paper 0 (DOI: 10. 5281/zenodo. 17852167, published in Int. J. Quantum Found. 12 (2), 667-718, 2026).