Constructive Verification of K = 12 Lattice Saturation Exploring Kinematic Consistency in the Selection-Stitch Model

The Selection-Stitch Model (SSM) proposes a view of the vacuum not as a pre-existing back- ground arena, but as an emergent geometry constructively built from discrete topological operators. A persistent challenge in modeling discrete kinematics is “geometric frustration,” where local assembly rules frequently yield disordered, porous foams rather than a smooth, saturated spatial bulk. In this study, we resolve this structural bottleneck by applying the Holographic Principle directly to the generative kinematics. We demonstrate computation- ally that when vacuum assembly is governed by 2D-dominant lateral growth—grounded in the requirement that the minimal physical gauge-invariant entanglement structure is a closed triangular loop [7]—and driven by a rigorous e−3 ≈ 4.98% topological tunneling probability [8], the three-dimensional network naturally crystallizes into a polycrystalline Face-Centered Cubic (FCC) Cuboctahedral geometry governed by the Kepler kissing num- ber theorem [4]. At N = 5000 nodes, this holographic algorithm achieves a global mean ¯ coordination of K = 9.83, with K = 12 emerging as the modal structural state (41.1% of the lattice). Furthermore, the emergent square faces of the lattice precisely resolve the δ≈7.36◦ Regge deficit angle inherent to tetrahedral tiling. Applying the derived bare kinematic limit (1/√3 ≈0.577L) yields a theoretical macroscopic compactness bound (Cmax ≈0.242) that is in falsifiable tension with current neutron star observations, while simultaneously predict- ing the exact geometric elimination of classical black hole singularities at r= 1.5Rs. These results confirm that 3D spatial reality in the SSM manifests fundamentally as a holographic projection of stacked 2D boundaries.