Q_tilde_e
The definition sets the integerized electron charge to -6 by negating the cube-face scale k=6. Researchers deriving the lepton index Z_ℓ=1332 from the even polynomial ansatz cite it as the direct input to that calculation. It is a one-line abbreviation that applies the upstream integerization_scale definition.
claimThe integerized electron charge is defined by $Q̃_e := -k$, where $k=6$ is the integerization scale given by the number of faces of a 3-cube.
background
The Z-Map Derivation module converts the electron charge Q_e=-1 into an integer via the scale k=cube_faces(3)=6, one independent 2D symmetry channel per face of the 3-cube. This produces the integerized charge Q̃_e = k · Q_e = -6. The upstream definition integerization_scale supplies this scale as a geometric structural input documented separately from the T0–T8 forcing chain.
proof idea
This definition is a one-line abbreviation that negates the integerization_scale value after casting it to ℤ.
why it matters in Recognition Science
This definition supplies the input charge index for the even polynomial Z(Q̃)=a Q̃² + b Q̃⁴ with minimal coefficients (a,b)=(1,1), which produces Z_ℓ=1332. It is used by the equality theorem Q_tilde_e_eq and the consistency check Z_lepton_matches_anchor_value that confirms the derived value matches the hardcoded anchor. The construction ties the geometric cube-face count to the lepton mass ladder in Recognition Science.
scope and limits
- Does not derive the integerization scale k from the T0-T8 chain.
- Does not compute the full Z polynomial or its coefficients.
- Does not address higher-generation leptons or other particles.
Lean usage
theorem Z_lepton_matches_anchor_value : Z_poly 1 1 Q_tilde_e = 1332 := by simp [Z_poly, Q_tilde_e, integerization_scale_eq]formal statement (Lean)
45def Q_tilde_e : ℤ := -(integerization_scale : ℤ)
proof body
Definition body.
46