Cosmology Through Constraint Geometry: A Zero-Parameter Derivation of Fundamental Constants from Topological First Principles

Abstract: We present the cosmological application of the Constraint Geometry Framework (CGF), in which physical structure emerges from accumulated geometric constraint rather than eternal laws. The framework rests on four pillars: (1) Viscous Differentiation—Type II universes separate from parent black holes through geometric extrusion; (2) Master Equation—a single evolution equation governs constraint dynamics, producing all large-scale structure; (3) Kissing Number Topology—the n=13 threshold emerges from the geometric impossibility of fitting more than 12 equal spheres around a central sphere; (4) Resonance/Attractor Dynamics—continuous Kerr input is filtered into discrete quantum output via standing-wave selection, explaining how General Relativity produces Quantum Mechanics. The framework achieves zero free parameters. All physical constants derive from pure topology: the kissing number (n=12) generates icosahedral symmetry, which produces the n=13 materialization threshold and the ℓ=7 chiral breach. From these emerge: the hierarchy ratio v/MPl = (7π/2) e^ (-13π) (0. 41% accuracy), the fine structure constant α⁻¹ = 14π² (1-δ) (0. 04% accuracy), dark energy Ω_Λ = 2/3 + 2δ (0. 35% accuracy), and the Hubble tension resolution via quadrupole strain ε = 1/13. The framework distinguishes Type I universes (primordial, isotropic) from Type II (Kerr-born, anisotropic). Our universe is Type II, inheriting threshold hierarchy, helical structure, and torsion-driven expansion from its parent black hole. We reinterpret the dark sector: Dark Matter is sub-threshold constraint carving—uncollapsed creative potential that exhausts near baryonic matter. Dark Energy is parental torsion relaxation. The "missing 95%" is misattributed geometry. All matter is baryonic. The quantization mechanism is not metaphorical: discrete particles emerge from continuous spacetime exactly as Chladni patterns emerge from continuous bow strokes—through resonant mode selection on a topologically constrained manifold.