The Universal Cascade Law: A Universal Law of Geometric Organization in Nonlinear Systems

Complexity mathematics was founded in the late nineteenth century to classify all nonlinear systems by their geometric architecture. For forty years, the field narrowed its focus to a single equation family, leaving the classification of multidimensional nonlinear coupled systems unperformed. The MESA Method recovered the original program and was applied to nineteen equation systems across general relativity, particle physics, fluid dynamics, statistical mechanics, astrophysics, and biology, with zero refutations. Empirical confirmation was obtained via the European Space Agency Gaia Data Release 3 stellar catalog, where Feigenbaum sub-harmonic analysis of 5,000 stars revealed dual-attractor basin structure at…