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 $M^5$ 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 ($\beta \to 1$) 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 $\beta = 0.95c$, where it begins to exhibit a localized grid-shear drift (the energy split widening from $10^{-11}$ to $10^{-9}$ at $\beta = 0.99c$). 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.
Publication Date: 2026-06-14