IndisputableMonolith.StandardModel.WeakCoupling
The WeakCoupling module defines the weak coupling constant α_W via the tree-level electroweak identity α = α_W sin²θ_W. It supplies auxiliary lemmas for positivity, ordering relative to α, and a certification object. Electroweak modelers in Recognition Science cite it when linking the alpha band to boson masses. The module consists of direct definitions drawn from imported constants together with short algebraic expansions.
claim$α_W = α / sin²θ_W$, where $α$ lies in the Recognition Science alpha band and $θ_W$ is the weak mixing angle; auxiliary results establish $α_W > 0$ and $α_W > α$.
background
Recognition Science obtains all constants from the phi-ladder and the J-cost function. The Constants module fixes the fundamental time quantum τ₀ = 1 tick. The Alpha module constrains 1/α to the narrow interval (137.030, 137.039). ElectroweakMasses places the Z boson at rung 1, yielding the mass formula m_Z = 2 φ^{51} / 10^6 MeV. The present module applies the tree-level relation α_EM = α_W sin²θ_W to introduce the weak coupling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the weak coupling definition required for electroweak unification calculations inside the StandardModel domain. It bridges the alpha band of Constants.Alpha to the mass predictions of ElectroweakMasses and supports later coupling comparisons. No downstream theorems are recorded yet, but the construction fills the tree-level identity in the Recognition Science forcing chain.
scope and limits
- Does not derive sin²θ_W from the J-function or forcing chain.
- Does not incorporate loop corrections or running of couplings.
- Does not predict a numerical value for α_W beyond the defining relation.
- Does not address the strong coupling or neutrino sector.