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

This framework paper unifies the five companion projects of the SL(6,ℂ) cosmological programme—CGICE geometric–information dynamics, three-spacetime-phase evolution, right-handed neutrino condensation and time-charge duality, the light-speed interface, and gravitational waves from spacetime-phase evolution—through their common gravitational structure. Within a framework inspired by $SL(6, \mathbb{C})$, we explore the mutual consistency of the metric signature, reduction map, clock, and stress-energy tensor via statistical geometry, thereby determining the physical spacetime. Given a separate six-dimensional metric of inertia (5,1), an integrable positive rank-two vertical bundle and a projectable horizontal metric, a Schur-complement construction yields a four-dimensional Lorentzian quotient. We identify a finite effective-field-theory window and derive the scalar characteristic cone and background constraint propagation from a common action. A root-potential diffusion supplies explicit statistical rates and a conditional branching relation. The finite error-composition result composes occupation errors, source-covariance errors and background-response errors into a finite observable bound. A three-state ensemble realizes the composition, while a retarded-propagator estimate connects response uncertainty to the background geometry. All physical parameters remain free inputs, and the net predictive content of this paper is a finite error-composition theorem together with consistency conditions that can reject a model. Dynamical real-section selection and a self-consistent interacting quantum cosmology remain further problems.