Cosmic Geometric Information Dynamics: A Conditional SL(6,C) Model with Explicit Spectral, Stochastic and Formalization Boundaries

We develop a conditional geometric-information dynamics model on the Riemannian configuration space X_E=SL(6,C)/SU(6), with interfaces to a separately supplied four-dimensional Lorentzian effective theory. Free-Laplacian thresholds, weighted-diffusion gaps and mediator masses are distinguished. A charged scalar phase provides a dynamical clock candidate after an explicit matching choice; finite clock range can obstruct relaxation. Measured-space flux-force conjugacy, a quartic stationary-current witness and martingale expectations contribute moment-functional (not full relative-entropy) steps to the mathematical core, and the quartic hierarchy shows Gaussian closure is not dynamically invariant. A specified positive mediator spectrum conditionally bounds an attractive coupling and yields a neutral-condensation exclusion criterion without determining CP violation. A spatial response map and noncollinear seeds are required to bridge covariance with gravitational-wave stress. An independent classical instanton endpoint yields the BPS bound and unit BPST action 8π²/g² without the D1 matching premise; actual coordinate curvature connects to the retained integral endpoint under a stated polar-measure identification. Independent Rayleigh comparators, an exactly solved finite heat semigroup and conditional correction budgets make further proof obligations testable, and a sextic potential supplies a constructive vacuum benchmark. Continuum stochastic construction, the geometric spectral theorem, quantum stress and observational matching remain stated obligations.