Viscous Dynamics on the Almost Hermitian Manifold: Deriving Quantum Mechanics from Non-Integrable Geometry

We present a rigorous geometric framework that unifies spacetime topology with quantum dynamics by relaxing the Riemannian axiom of a torsion-free connection. We define the physical vacuum as an Almost Hermitian Manifold $\mathcal{M} \cong \mathbb{C}^4$ governed by the Chern connection, which preserves the non-integrable complex structure $J$ at the cost of non-vanishing Torsion. We demonstrate that the Schrödinger Equation emerges naturally as the linear hydrodynamic limit of a stochastic diffusion process driven by the imaginary sector of the Torsion tensor (the Lee Form). Furthermore, we prove via Hurwitz's Theorem on Composition Algebras and Adams' Theorem on Parallelizability that the maximal dimensionality of a causal, unitary vacuum is constrained to 8 real dimensions ($\mathcal{V} \cong \mathbb{O}$), with 4-dimensional spacetime emerging as a Lagrangian submanifold. This framework resolves the "measurement problem" by identifying $\hbar$ with the kinematic viscosity of the symplectic manifold, rendering quantum non-locality a consequence of symplectic rigidity (Gromov's Theorem).