A Hybrid Linear-Oscillatory Framework for System Dynamics.

This paper presents the Universal Oscillating Path, a recursive mathematical framework based on the premise that the linear equation (𝒚 = 𝒎𝒙 + 𝒃) constitutes the fundamental structural unit of all physical laws. While classical systems maintain linear stability, complex environmental systems exhibit chaotic fluctuations. This model bridges the gap by integrating a Logarithmic Translator to linearize exponential complexity and a dynamic feedback loop to account for White Events (stochastic shocks). The framework is designed for multi-stage modelling where the output of one linear iteration serves as the input for the next, representing continuous environmental feedback loops.