Closing Five Structural Gaps in the Relativistic Stochastic Coherence Framework

We close five structural gaps identified in the relativistic extension of the stochastic coherence framework. First, we prove that the projected noise correlator is the unique tensor structure consistent with Lorentz covariance, rest-frame spatiality, and correct rank. Second, we show that the boost-spin decomposition used for pedagogical identification of terms in the Hamilton-Jacobi equation is not required by any of the main theorems: orbital quantization, recovery of the Dirac equation, and the spin-statistics connection all hold for arbitrary (non-irrotational) flow. Third, we establish that for stationary points of the Onsager-Machlup functional with finite action, the nodal set generically consists of smooth worldtubes of codimension 3, with possible singularities confined to a subset of codimension 4 or greater, extending the domain of validity of the orbital quantization theorem to all physically relevant configurations. Fourth, we construct the explicit N-body Onsager-Machlup action on the many-body configuration space, prove that orbital quantization holds particle by particle, and extend the spin-statistics connection to arbitrary N: the Pauli exclusion principle emerges as a consequence of non-negative probability density and the topology of the Spin(1,3) group, without a symmetrization postulate. Fifth, we extend the entire framework to curved spacetime: we construct the covariant Onsager-Machlup action on spin manifolds, prove that orbital quantization survives curvature (as an ultralocal mechanism), recover the curved-spacetime Dirac equation, and show that the framework predicts that physical spacetimes must admit spin structures. Furthermore, the exact off-shell equivalence of the stochastic stress-energy tensor guarantees a mathematically consistent semiclassical backreaction.