subcellCount_edge

The module derives fermion generation torsion from the CW-filtration of the spatial 3-cube $Q_3$. Subcells are typed as vertices (CW-dim 0), edges (CW-dim 1), and faces (CW-dim 2). The total count of each type is packaged by subcellCount, which dispatches to the standard hypercube formulas: $2^d$ vertices, $d\cdot 2^{d-1}$ edges, and $\binom{d}{2}\cdot 2^{d-2}$ square faces.

Spatial dimension is fixed at $D = 3$ by the forcing chain (T8 / linking). At that value the 1-skeleton has twelve edges, of which eleven are treated as passive field edges in the cumulative torsion schedule. The module premise is that generation excitations couple to subcells in increasing CW dimension, so the edge count enters the Gen-2 torsion step.

One-line computational proof: native_decide unfolds subcellCount D .edge to the edge-count formula at $D = 3$ and checks equality with $12$. No lemmas are invoked beyond definitional reduction of the cube-edge closed form.

Supplies the numeric 1-skeleton size used throughout the excitation-ordering argument. With eight vertices and six faces, the twelve edges underwrite the intermediate torsion value $11$ (passive field edges) in the schedule ${0, 11, 17}$ that the module aims to recover from CW dimension alone. That schedule is the geometric reason edges precede faces in CubeAdmissibleTorsion, replacing ad-hoc mode labels by filtration order. The result sits under the Masses domain and supports the J-cost strict ordering $J(\varphi^0) < J(\varphi^{11}) < J(\varphi^{17})$ once the filtration premise is granted. No downstream theorems currently depend on it in the graph; it is a local simp fact for the module's own passive-coupling lemmas.