anchor_electron_Z
The electron charge index evaluates to 1332 under the lepton-sector formula of ZOf. Researchers modeling lepton masses on the phi-ladder cite this fixed anchor when placing the electron rung. The proof is a one-line reflexivity that evaluates the definition of ZOf on the electron.
claim$Z(e) = 1332$, where $Z$ is the lepton charge index given by $q^2 + q^4$ evaluated at the integerized charge $q = -6$.
background
The Z-map assigns an integer charge index to each fermion. For leptons the index follows the even polynomial $Z = q^2 + q^4$ with $q = tildeQ(f)$, while quarks receive an extra offset of 4. The integerization step sets $tildeQ_e = 6 times (-1) = -6$, where the prefactor 6 equals the face count of the 3-cube and supplies one independent 2D symmetry channel per face. This construction is stated as a geometric structural input rather than a consequence of the T0-T8 forcing chain.
proof idea
The proof is a one-line reflexivity that directly evaluates the definition of ZOf on the electron fermion.
why it matters in Recognition Science
This theorem supplies the concrete anchor value 1332 for the electron in the Z-map derivation. It supports the sibling results on Z_lepton_eq and Z_lepton_decomposition that decompose the lepton indices. Within the Recognition framework it fixes the starting rung for the electron mass formula yardstick times phi to the power (rung minus 8 plus gap(Z)), closing the charge-integerization step that precedes the phi-ladder mass assignments. The module notes that the face count k=6 is a geometric input rather than a consequence of the T0-T8 forcing chain.
scope and limits
- Does not derive the cube-face count k=6 from the forcing chain T0-T8.
- Does not compute the integerized charge for other fermions.
- Does not address the physical interpretation of the Z index beyond the polynomial ansatz.
- Does not connect to the fine-structure constant alpha or the eight-tick octave.
formal statement (Lean)
96theorem anchor_electron_Z : RSBridge.ZOf .e = 1332 := rfl
proof body
Term-mode proof.
97
98/-- All three leptons share the same charge index. -/