Constructive Verification of K = 12 Lattice Saturation Demonstrating the Geometric Consistency of the Selection-Stitch Model

Discrete kinematic models of spacetime, such as tensor networks and causal dynamical triangulations, frequently encounter the problem of geometric frustration: local probabilistic assembly rules tend to yield disordered, porous graphs rather than structurally saturated volumetric bulks. In this study, we investigate the kinematic growth of a discrete spatial network governed by a strict exclusion radius and proximity entanglement rules. We demonstrate computationally that imposing a strongly 2D-dominant lateral growth algorithm—where out-of-plane nodal projections are exponentially suppressed by the codimension difference between the 2D Stitch (1-parameter solution manifold) and 3D Lift (0-parameter pair) operators, yielding P_lift = e^-3—resolves this geometric frustration. This suppression amplitude receives a second, independent motivation from quantum error correction: the emergent FCC lattice supports a [[192,130,3]] CSS code whose distance d = 3 sets the survival threshold for out-of-plane nodes at exactly e^-d = e^-3. Under these constraints, the three-dimensional network undergoes the kinematic cascade K = 1 → K = 6 → K = 4 → K = 12, escaping the geometrically frustrated K = 4 tetrahedral foam (Regge deficit δ ≈ 7.36°) and crystallizing into a polycrystalline Face-Centered Cubic (FCC) lattice that saturates the Kepler kissing-number bound (K = 12). A bulk-interior diagnostic—based on the strict crystallographic criterion that a node has at least 42 neighbors within radius 2L (its three full FCC coordination shells)—establishes that the bulk modal coordination is exactly K = 12 at every system size from N = 250 upward, providing direct (non-extrapolated) evidence of FCC bulk crystallization. The all-node K = 12 fraction follows the surface-to-volume scaling f = 1 - (6.8 ± 0.6) N^(-1/3), confining under-coordinated nodes to the cluster surface (30 seeds per size). A parameter sweep over lift probability identifies an optimal band p ∈ [3%, 5%] for the volumetric yield Φ = f_{K=12} × (z_ext/xy_ext), with e^-3 sitting inside this band; both lower and higher lift rates are clearly degraded. The simulation demonstrates exact layer planarity (σ_z < 10^-10 L) and uniform FCC inter-layer spacing (0.8165 ± 0.0011 L). We analyze the network's sensitivity to the exclusion radius, identifying a strict geometric failure threshold at R_ex = 1/√3 L that induces structural jamming, with a wide stability plateau across R_ex ∈ [0.58, 0.99] L confirming that operating values are not fine-tuned.