Emergent Three-Dimensional Lattice Saturation at K = 12 via Geometric Exclusion in Discrete Networks - Selection Stitch Model Simulation

The Selection-Stitch Model (SSM) proposes that the vacuum of space-time emerges from a discrete pre-geometric network. A central prediction of this framework is the spontaneous saturation of the bulk lattice at a local coordination number of K = 12, corresponding to the kissing number in three-dimensional Euclidean space. In this work, we present a first-principles computational verification of this limit. Using a constructive simulation of 5,000 nodes governed solely by a unitary exclusion principle (Hard Shell R ≥ 0.95L), we demonstrate that the network naturally evolves from a high-entropy surface phase into a saturated bulk phase. The simulation results show a maximum local degree of exactly 12 in the dense interior, with attempts to form a 13th neighbor consistently rejected by geometric constraints. This confirms that the lattice saturation predicted by SSM is an inevitable consequence of packing discrete information in 3D space, rather than an arbitrary parameter.