Emergent Lorentz Symmetry in the U-Cell Model: A Wilson RG Attractor with Global Lyapunov Stability

In the Standard Model, Lorentz symmetry is postulated. The U-Cell Model (UCM) derives it as an infrared fixed point of the Wilson renormalisation group. The substrate lattice generates a unique coupling L_cov between matter fields and the substrate displacement. A four-step one-loop RG calculation shows that this coupling drives every matter-field velocity c_i toward the substrate sound speed c_0 exponentially: d(c_i² - c_0²)/dℓ = -κ_RG(c_i² - c_0²), with κ_RG = 5c_0/(108π²a³) > 0. The Lyapunov functional V_i = (c_i² - c_0²)² ≥ 0 satisfies dV_i/dℓ ≤ 0 with equality only at c_i = c_0, establishing global stability without fine-tuning for all initial conditions c_i(0) > 0. The fixed point c_0 is self-consistent (dc_0/dℓ = 0). The attractor holds for all spins s = 0, 1/2, 1, 3/2, 2. Non-perturbative stability is confirmed by the Wetterich functional RG equation with an η_μν-covariant Litim regulator: the coupling ratio α:β = -1:+1 is exactly preserved at all RG scales via O(4)-covariance of the regulated propagators and substrate momentum conservation, without any fine-tuning or order-by-order cancellation. The Lorentz-violating deviation Δ_i is treated as a perturbative vertex insertion, allowing an unambiguous Wick rotation on the universal c_0 background. The quantisation of the substrate itself remains an open problem.