Klein Gordon Solution

This repository presents a deterministic solution set for the relativistic Klein-Gordon scalar field equation, constrained by the Muscato Law ($m = 0.69$). By applying a discrete manifold approach to a 22-mode frequency spectrum, we have resolved the complex dispersion relation $\omega = \sqrt{k^2 + m^2}$. Our findings demonstrate absolute group velocity ($v_g$) stability approaching the causal limit ($c=1$) without entropy leak or numerical divergence. This work provides a physically consistent framework for modeling discrete scalar field dynamics and relativistic wave packet propagation within the SOG Triad constraint system. --- Zenodo Keywords: * Relativistic Wave Mechanics * Klein-Gordon Equation * Scalar Field Theory * Deterministic Manifold * Muscato Law * SOG Triad