Statistical Dynamics and Conditional Lorentzian Reduction in an SL(6,C)-Motivated Cosmological Framework

We study the interfaces required to connect an SL(6,C)-motivated statistical geometry to a four- dimensional Lorentzian effective theory. A neutral six-dimensional metric admits three orthogonal four-plus-two inertia allocations without establishing three dynamical spacetime phases, and the pos- itive covariance compression does not select Lorentzian signature. A separate positive-fiber branch permits conditional Lorentzian reduction and a finite internal-mode cutoff. We construct a nonstation- ary reflecting diffusion benchmark whose cell occupations are actual probability integrals and whose derivatives equal boundary fluxes. For a three-well potential, we construct the normalized station- ary Gibbs density and bound a concrete resistance integral. Finite stochastic propagation yields an accumulated occupation-error bound, while finite cumulative activity leaves a quantified memory of the initial state. An explicit finite cohomology quotient carries a positive descended pairing. Within the supplied Lorentzian action, conservation, mediator bounds, charged equilibria, and tensor-source constraints retain their stated domains. A finite covariance construction controls quadratic response errors. These results strengthen individual interfaces but establish no shared cosmological solution, quantum state space, or observational prediction. A complete emergence claim still requires con- trolled metastable projection, calibrated time, dynamical reduction, coupled stress evolution, and source matching.