UCM 47: Canonical Commutation Relations from the Substrate Path Integral

We show that the canonical commutation relations of quantum mechanics follow from a structural property of the U-Cell Model substrate: the free action is exactly quadratic, making the substrate a system of coupled harmonic oscillators. Fourier decomposition into normal modes, followed by the Stone-von Neumann theorem, yields unique commutation relations with no free parameters. The anharmonic gravity-matter coupling does not modify the result, because the symplectic structure depends only on the kinetic term. One irreducible postulate remains: that the substrate fluctuates. Given this empirical fact, the structure, scale, and uniqueness of quantum mechanics follow from the substrate without further input. This closes Open Problem 2 of the UCM Mathematical Companion (Part Q).