integerization_scale
The integerization scale k is defined as the face count of the 3-cube, yielding k=6. Researchers deriving the lepton index Z_ℓ=1332 via charge integerization cite this when constructing the scaled electron charge Q̃_e = k · Q_e. It supplies one independent 2D symmetry channel per face of Q₃ as a geometric input. The definition is a direct specialization of the cube_faces function to dimension 3.
claimLet $k$ be the integerization scale, defined by $k := F(3)$ where $F(D)$ counts the faces of the $D$-cube and $F(3)=6$.
background
The Z-map derivation module constructs the lepton charge index Z_ℓ=1332 from charge integerization followed by an even polynomial ansatz. Charge integerization sets k=F(3)=6, where each face of the 3-cube Q₃ supplies one independent 2D symmetry channel for quantizing charge. This k then scales the electron charge to the integerized value Q̃_e = k · Q_e = -6. Upstream definitions of cube_faces agree on the value 6 for D=3: one states F=2D, another notes the 3-cube has 6 faces, and a third gives the explicit match for D=3.
proof idea
One-line definition that applies the cube_faces function to the argument 3.
why it matters in Recognition Science
This definition supplies the scaling constant k=6 that produces Q̃_e=-6, which then enters the minimal even polynomial Z(Q̃)=Q̃² + Q̃⁴ to give Z_ℓ=1332. It fills the first step of the Z-map derivation and is referenced by the equality theorem integerization_scale_eq and the definition Q_tilde_e. The module treats the face count as a geometric structural input rather than a consequence of the T0-T8 forcing chain.
scope and limits
- Does not derive the face count from the T0-T8 forcing chain.
- Does not specify a dynamical mechanism for the symmetry channels.
- Does not generalize the construction to other dimensions or charges.
Lean usage
def Q_tilde_e : ℤ := -(integerization_scale : ℤ)formal statement (Lean)
40def integerization_scale : ℕ := cube_faces 3
proof body
Definition body.
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