The Selection-Stitch Model (SSM) relies on a specific vacuum geometry (K= 12) to resolve the Hubble Tension. This paper addresses the fundamental critique: Is this geometry arbitrary? By mapping the "packing" of quantum information to the Sphere Packing Problem, we utilize the proof of the Kepler Conjecture to show that the Cuboctahedron is a thermodynamically favored ground state. We further argue that symmetry requirements select the Face-Centered Cubic (FCC) lattice over the alternative Hexagonal Close Packing (HCP).