Deterministic Cosmic Architecture: Linking Global Dark Matter and Local Star Formation through Carrollian Freezing

We introduce a multi-scale geometric framework that patches General Relativity's classical breakdown threshold at the singularity limit without invoking exotic extensions, hidden dimensions, or undiscovered subatomic fields. Guided by the principles of the Belinski-Khalatnikov-Lifshitz (BKL) conjecture, we show that a 10^{56} geometric volumetric contraction inside collapsing 10^{11} kg primordial masses drives an instantaneous Carrollian phase transition (c \to 0) at the end of inflation (t = 2.47 \times 10^{-25} s). This metric degeneracy enforces a strict coordinate velocity clamp (dx^i/dt = 0), regularizing curvature invariants while preserving a stable, non-radiating, macroscopically isolated gravitational mass footprint. Distributed as a global, collisionless background matrix spaced at a sparse mean interval of \sim 24 AU, these remnants naturally account for 100% of the cosmic Cold Dark Matter budget, safely evading optical micro-lensing survey limits. Crucially, our framework derives the cosmic value of the speed of light not as an arbitrary constant, but as a rigid boundary condition fine-tuned to act as a geometric circuit breaker at the Tolman-Oppenheimer-Volkoff (TOV) nuclear failure limit. On galactic scales, localized remnant overdensities clustered at a 215-meter separation profile resolve the Core-Cusp problem and form an extended, zero-feedback gravitational sponge. The resulting quadratic accretion cascade (\dot{M}_b \propto M_{\text{effective}}^2) suppresses the localized radiation pressure gradient (\lim_{c \to 0} P_{\text{rad}} = 0), providing a direct geometric solution to the anomalous "X-ray Weakness" and accelerated mass assembly observed across high-redshift JWST Little Red Dot (LRD) galaxies. Scaled down to stellar systems, the framework dictates that single remnants drop the local Jeans mass to zero, driving the binary mass divergence between main-sequence stars and core-accretion gas giants, matching active helioseismology data tracking low-frequency gravity modes. We conclude with clear proposals for experimental falsifiability via LISA orbital dephasing and Roman Space Telescope weak-lensing micro-flecking maps.