IndisputableMonolith.RSBridge.ZMapDerivation
ZMapDerivation module defines the integerization scale with one channel per cube face in the cubic ledger. It supplies Z-polynomials, lepton decompositions, and equality statements that align with anchor values. Recognition theorists mapping the phi-ladder to Standard Model fermions would cite these constructions. The module consists of definitions and direct equality lemmas.
claimThe integerization scale satisfies one channel per cube face. The Z-polynomial is even with a zero at the origin; the lepton decomposition matches the anchor value via $Z_l = q̃^2 + q̃^4$.
background
The module sits in the RSBridge domain and imports AlphaDerivation together with Anchor. AlphaDerivation supplies the structural derivation of α^{-1} via 4π from Gauss-Bonnet on vertex deficits of Q₃. Anchor defines the 12 fermions, the charge-indexed integer ZOf = q̃² + q̃⁴ (+4 for quarks), the gap function F(Z) = ln(1 + Z/φ)/ln(φ), and massAtAnchor at scale μ⋆.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the Z-map constructions into RSBridge.Anchor for fermion species and gap applications. It supplies the integerization step required to place recognition costs on the phi-ladder and connect to the T5–T8 forcing chain and the RCL identity.
scope and limits
- Does not derive numerical masses for all 12 fermions.
- Does not treat quark sectors beyond the ZOf definition.
- Does not prove uniqueness of the integerization scale.
- Does not address boson or gauge sectors.
depends on (2)
declarations in this module (15)
-
def
integerization_scale -
theorem
integerization_scale_eq -
def
Q_tilde_e -
theorem
Q_tilde_e_eq -
def
Z_poly -
theorem
Z_poly_even -
theorem
Z_poly_zero -
theorem
minimal_coefficients -
theorem
unit_coefficients_minimal -
theorem
Z_lepton_eq -
theorem
Z_lepton_decomposition -
theorem
Z_lepton_matches_anchor_value -
theorem
anchor_electron_Z -
theorem
leptons_same_Z -
theorem
Z_poly_strictly_increasing