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 the Cayley-Dickson construction 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).