integerization_scale
plain-language theorem explainer
The integerization scale sets k to the face count of the three-cube. Derivations of the lepton charge index Z_ℓ = 1332 cite this scale when converting the electron charge to an integer multiple. The definition applies the hypercube face function directly at dimension three.
Claim. Let $F(D)$ denote the number of faces of the $D$-dimensional hypercube. The integerization scale is defined by $k := F(3)$.
background
The Z-map derivation module constructs the lepton index from charge integerization followed by an even polynomial ansatz. Charge integerization introduces one independent 2D symmetry channel per face of the three-cube Q₃, with the face count supplied by cube_faces. Upstream definitions give cube_faces(D) = 2D, so the value at D=3 is six; the module treats this count as a geometric structural input rather than a result derived from the T0-T8 chain.
proof idea
The definition is a direct one-line application of cube_faces at argument 3.
why it matters
This definition supplies the integerization factor k that feeds integerization_scale_eq and Q_tilde_e. Those results enable the even polynomial Z(Q̃) = a Q̃² + b Q̃⁴ with minimal coefficients (a,b)=(1,1) that yields Z_ℓ=1332. The module presents the face count as the geometric input required for charge quantization in the Z-map construction.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.