Convergence: The Universal Cascade Law in the Infinite-Dimensional Limit

Description/Abstract: The Quantum Emergence Theorem (Math Paper 4) proved that the Universal Cascade Law's self-grounding property extends across the quantum-classical boundary, completing a five-layer universality hierarchy. That paper noted three technical convergence questions in its open remarks: stability of quantum observables in the infinite-dimensional Hilbert space limit, the progressive emergence of the Feigenbaum cascade as the system transitions from quantum to classical, and quantification of the cascade whisper in quantum fluctuations. This paper answers all three. The quantum phase transition at γ_q = 1.1838 converges to six decimal places by N = 30 Fock states and is unchanged through N = 50 —…