Resolution Geometry: From the Birth of the First Bit to the Death of the Last Black Hole

This paper proposes a foundational framework for cosmology based on two information-theoretic axioms: Exchange-Consistency (identity must be intrinsically encoded) and Finite Distinguishability Capacity (information density is bounded by surface area). From these premises, we demonstrate that the laws of physics—including General Relativity and Quantum Mechanics—emerge as necessary theorems of identity management under finite constraints. The central contribution of this version is the rigorous derivation of the Dark Matter to Baryonic Matter mass ratio without free parameters. By modeling the 3D universe as a cellular foam emerging from a 2D scaffold, we identify "Dark Matter" as the structural tension required to close 3D volumes (pentagonal frustration) against the 2D efficiency optimum (hexagonal tiling). Utilizing the Aboav-Weaire law for random foams, we derive a theoretical mass ratio of Ωdm/Ωb ≈ 5. 32, consistent with Planck 2018 observations (5. 36) to within <1%. Furthermore, we demonstrate that the "Hubble Tension" is resolved as a phase transition in scaffold management at z ≈ 1. 5, predicting a specific "cosmic jerk" detectable by next-generation surveys (DESI, Euclid, Roman). The framework also explains why no Dark Matter particle has been detected: Dark Matter is not particulate but a continuous tension field inherent to 3D geometry itself. This paper proceeds in two passes. The main text (Parts I–VII) develops the framework through logical argument, building each layer from its predecessors and connecting to observable physics. The Appendices then formalize these arguments mathematically: Appendix A constructs the full inheritance chain from Boolean algebra through cosmology. Appendix B derives General Relativity as a cost-minimization theorem. Appendix C proves the Dark Matter ratio from topological constraints. Readers seeking the formal derivations should note: the math is in the back because it follows from the logic, not the other way around. That's how it was built, logic first. The math simply fit.