The persistent crises in modern cosmology—the Hubble Tension, anomalous galactic rotation curves, dynamically decaying Dark Energy, and the ad-hoc parameterization of Cosmic Inflation— indicate a fundamental structural failure in continuous spacetime models. We propose a rigorously discrete 7-dimensional manifold (6S + 1T) wherein the observable universe is a positively curved 3D boundary, tessellated by the Poincar´e Dodecahedral Space (PDS) and embedded within a 6-dimensional spatial bulk. By separating mass-anchored metric expansion from photonic bulk refraction, we resolve the Hubble Tension as a topological optical artifact (72.26 km/s/Mpc vs 69.8 km/s/Mpc), preserving local Lorentz invariance. We establish a first-class Dirac constraint algebra to guarantee vacuum stability across the extra dimensions and derive the 7D Generalized Friedmann Equations to naturally yield geometric Dark Energy (Λ = 0). Natively calculating the lattice bifurcation of the boundary yields a purely geometric equation of state for Dark Energy (w0 ≈ −0.809) that precisely matches 2024 DESI constraints. Finally, we map Baryogenesis, Cosmic Inflation, and the exact ϕ-scaled mass hierarchy of the neutrino to the chiral geometric projection of the 6D bulk.