IndisputableMonolith.Unification.GaugeCouplingsComplete
This module assembles the complete set of gauge couplings in Recognition Science by importing derivations for the electromagnetic, strong, and weak sectors. A physicist constructing low-energy Standard Model parameters from cubic ledger geometry would cite it for the unified constants. The structure composes prior results from AlphaDerivation, StrongForce, and WeinbergAngle without introducing new proofs.
claim$\alpha = 1/(4\pi \cdot 11 \cdot \exp(f_{\rm gap}/(4\pi \cdot 11)))$ with $\alpha^{-1} \approx 137.036$, $\alpha_s(M_Z)$ from planar symmetries, and $\sin^2 \theta_W ≈ 0.2229$ from $\phi$-structure.
background
The module sits inside the cubic ledger geometry of AlphaDerivation, where 4π emerges from Gauss-Bonnet applied to vertex deficits of the 3-cube. It contrasts the full edge geometry used for the fine-structure constant with the planar symmetries that govern the strong coupling in StrongForce. The weak sector enters via the ϕ-based derivation of the Weinberg angle in the imported WeinbergAngle module, targeting the electroweak mixing parameter at the MZ scale.
proof idea
This is a definition module, no proofs. The argument proceeds by importing the four source modules and exposing their combined results through sibling declarations that certify each coupling and the overall C-014 certificate.
why it matters in Recognition Science
The module supplies the complete low-energy gauge couplings that close the C-014.1 electromagnetic derivation and support the broader unification program. It directly incorporates the cubic-geometry origin of α, the planar-symmetry origin of αs, and the ϕ-structure origin of θW, feeding these into any downstream unification statement.
scope and limits
- Does not derive the running of couplings with energy scale.
- Does not construct the full Standard Model Lagrangian.
- Does not prove gauge unification at a high scale.
- Does not compute loop corrections or higher-order effects.
depends on (4)
declarations in this module (11)
-
theorem
alpha_coupling_derived -
theorem
alpha_s_coupling_derived -
theorem
weak_mixing_phi_based -
theorem
coupling_geometric_factors -
theorem
coupling_formulas_distinct -
theorem
alpha_s_value -
theorem
weak_mixing_bounds -
theorem
alpha_s_within_pdg_bounds -
theorem
gauge_unification_hint -
theorem
coupling_distinction_low_energy -
def
C014_certificate