Numerical Verification and Cross-Domain Stress Testing of the Universal Oscillating Path (UOP)

This paper presents the numerical verification of the Universal Oscillating Path (UOP), a recursive mathematical framework designed to unify systemic dynamics across sixty orders of magnitude. By integrating a Logarithmic Translator and a Structural Resilience Parameter (S0), the model bridges the gap between quantum-scale fluctuations and macro-scale systemic collapses. This version documents the results of six rigorous stress tests—ranging from Planck-scale physics and Schwarzschild event horizons to malignant biological proliferation and geopolitical dissolution (Soviet Union).simulations demonstrate that the UOP formula maintains structural continuity near critical singularities, successfully identifying Deterministic Collapse Windows where informational friction (I) triggers non-linear systemic failure. The cross-domain success of these tests validates the UOP as a robust predictive tool for structural health, clinical prognosis, and systemic risk assessment, establishing a unified physical floor at the Planck scale (Epsilon) for all complex dynamical systems, while allowing the precision value to remain adjustable based on the desired accuracy and domain-specific requirements.