IndisputableMonolith.StandardModel.WeakCoupling
Module WeakCoupling supplies the definition of the weak coupling constant α_W = α / sin²θ_W together with positivity and ordering lemmas. Researchers working on electroweak unification and boson masses within Recognition Science would cite these constants. The module consists of definitions and elementary inequalities derived from the tree-level identity α_EM = α_W sin²θ_W.
claim$α_W := α / sin²θ_W$ where the tree-level identity gives $α = α_W sin²θ_W$.
background
This module sits in the StandardModel domain and imports the RS time quantum τ₀ = 1 tick from Constants, fine-structure definitions from Alpha, and the electroweak mass formula m_Z = 2 φ^51 / 10^6 MeV from ElectroweakMasses. It introduces the weak coupling via the tree-level electroweak identity α_EM = α_W sin²θ_W. The setting uses the Recognition Science phi-ladder and alpha inverse band (137.030, 137.039) to constrain coupling strengths.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies α_W for electroweak mass predictions and coupling hierarchies in the Recognition framework. It connects the alpha band to the weak sector through the mixing angle and supports downstream calculations on the phi-ladder. No parent theorems are recorded in the used_by edges.
scope and limits
- Does not derive sin²θ_W from the J-uniqueness or RCL.
- Does not include radiative corrections beyond tree level.
- Does not compute numerical values of α_W.
- Does not address the eight-tick octave or D = 3.
- Does not link to mass formula rung or gap(Z).