Discriminating Fundamental Substrates: A High-Velocity Simulation Benchmark for Continuous Field vs. Matrix-Grid Unification Theories

Standard Quantum Field Theory—specifically the Electroweak and Quantum Chromodynamics (EWT+QCD) sectors of the Standard Model—treats fundamental fermions as zero-dimensional point particles, necessitating complex statistical renormalization techniques to circumvent infinite self-energy divergences. Recently, two robust, deterministic alternatives have emerged to challenge this paradigm: the Ouroboros System (a classical Lagrangian field theory operating on a continuous Minkowski manifold) and the Affine Extension (AE) Liquid Crystal Model (operating on an M⁵ discrete matrix substrate). Intriguingly, both frameworks independently converge on a profound physical truth: time-periodic internal oscillation (a de Broglie clock / Zitterbewegung proxy) is energetically mandatory to stabilize localized matter, with the AE substrate demonstrating a discrete rest-energy minimization bound exactly 21% below its clock-stopped value. This paper introduces a rigorous computational benchmark designed to explicitly discriminate between these three competing visions of the universe. By subjecting localized excitations to a highly insulated, relativistic (1) dynamic sweep using co-moving phase gradients and Perfectly Matched Layer (PML) boundary conditions, we isolate clear numerical signatures. While EWT+QCD yields immediate self-energy infinities under deterministic dynamics, the discrete AE matrix substrate demonstrates excellent stability up to = 0. 95c, where it begins to exhibit a localized grid-shear drift (the energy split widening from 10^-11 to 10^-9 at = 0. 99c). This computational friction establishes a quantitative threshold, revealing exactly where a continuous field geometry like Ouroboros becomes a mathematical necessity to preserve true Lorentz invariance. We outline the codebase architectures and call upon the global computational and experimental communities to verify these limits.