We establish a classification of the fundamental equations of physics by a single geometric criterion: satisfaction of the three conditions of the Universal Cascade Theory (UCT). Any dynamical equation satisfying C₁ (dissipative boundedness), C₂ (non-degenerate quadratic fold), and C₃ (transversal spectral crossing) belongs to the Feigenbaum universality class and necessarily exhibits cascade architecture with constants δ = 4.66920160… and α = 2.50290787…. The Navier-Stokes equations, Einstein field equations, Yang-Mills gauge theory, the quantum Kerr oscillator, and the inflationary scalar field each satisfy these conditions by their functional form. The Null Theorem establishes that the linear Schrödinger equation categorically fails C₂. The Lovelock-Lucian Correspondence identifies a structural one-to-one mapping between the Lovelock uniqueness conditions for general relativity (L₁-L₃) and the UCT conditions (C₁-C₃). The Born rule |ψ|² is derived as the unique probability measure invariant under cascade renormalization in six lines, independent of Hilbert space axioms. This is not reductive unification — the forces are not one force. They are instances of one geometry.