integerization_scale_eq
The theorem establishes that the integerization scale equals six, the number of faces of a cube supplying independent symmetry channels for charge quantization. Researchers deriving the lepton charge index Z_ℓ = 1332 in the Recognition Science Z-map would cite this equality when integerizing the electron charge. The proof reduces directly to the definition via a native decision procedure.
claimThe integerization scale $k$, defined as the number of faces of the three-dimensional cube, satisfies $k = 6$.
background
The module derives the lepton charge index Z_ℓ = 1332 from charge integerization k = F(3) = cube_faces(3) = 6, integerized charge Q̃_e = k · Q_e = -6, an even polynomial ansatz Z(Q̃) = a·Q̃² + b·Q̃⁴, and coefficient minimality with (a,b) = (1,1). The upstream definition states: 'The integerization scale: one channel per cube face.' This supplies the structural input k for the subsequent steps that produce Z_ℓ = 1332 and match the anchor value.
proof idea
The proof is a one-line wrapper that applies native_decide to the definition integerization_scale := cube_faces 3.
why it matters in Recognition Science
This supplies the concrete value of the integerization scale used by Q_tilde_e_eq to obtain Q̃_e = -6 and by Z_lepton_matches_anchor_value to obtain Z_poly 1 1 Q_tilde_e = 1332. It fills the charge integerization step in the Z-map derivation, a geometric structural input documented as independent of the T0-T8 forcing chain.
scope and limits
- Does not derive the cube face count from the T0-T8 forcing chain.
- Does not generalize the scale beyond the three-dimensional cube case.
- Does not compute the full Z_ℓ polynomial or match the anchor value.
Lean usage
simp [integerization_scale_eq]formal statement (Lean)
42theorem integerization_scale_eq : integerization_scale = 6 := by native_decide
proof body
Term-mode proof.
43
44/-- The integerized electron charge: Q̃_e = k · Q_e = 6 · (-1) = -6. -/