We extend the stochastic coherence framework based on the Onsager-Machlup action to Minkowski spacetime. The configuration space R^n is replaced by M4, the scalar phase by a Lorentz rotor R in Spin+(1,3), and the observables by the four-current j^mu and spin tensor S^mu nu, both bilinear in R.We show that the combination of the relativistic stochastic Hamilton-Jacobi equation and the C^infty regularity of the bilinear observables over nodal surfaces forces the orbital winding number around nodal tubes to satisfy alpha = 2k with k a natural number, yielding orbital angular momentum quantized in integer multiples of h-bar: L = k in the non-negative integers. This establishes a strict topological separation between orbital angular momentum (determined by nodal regularity on the base manifold) and intrinsic spin (determined by the fiber group Spin+(1,3)).The variational derivation from the Onsager-Machlup action produces hydrodynamic equations that match the Takabayasi-Hestenes decomposition of the Dirac equation term by term. The derivation is non-circular: the dynamical constraint and the regularity requirement are logically independent.Additionally, we establish that the positivity condition rho >= 0 (inherent to any probability density) requires the internal orientation to be described by rotors in Spin+(1,3) rather than by SO+(1,3), as only the spinorial formulation guarantees a future-directed probability current. Finally, applying the Laidlaw-DeWitt decomposition to the many-body configuration space, we show that the double-cover structure of Spin+(1,3) fixes the exchange character to chi = -1 for spinorial representations, recovering Fermi-Dirac statistics without an independent symmetrization postulate.The framework remains within the domain of the free theory; extensions to curved spacetimes and many-body interactions are left for future work.