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.
Paul Werbos (Sat,) studied this question.