sin2ThetaW_RS
plain-language theorem explainer
The definition supplies the Recognition Science value of the Weinberg angle squared as (3 - φ)/6. Particle physicists checking electroweak precision would cite it to verify the predicted sin²θ_W lies inside the interval 0.228 to 0.232. The entry is a direct algebraic substitution of the golden ratio into the formula obtained from the Q₃ representation theory.
Claim. $sin^2 θ_W = (3 - φ)/6$
background
The module formalizes the representation theory of the quaternion group Q₃, which appears in Recognition Science as the symmetry group of the eight-tick cycle. Under electroweak symmetry breaking the four complex degrees of freedom of the Higgs doublet split into three Goldstone modes eaten by the W and Z bosons and one physical Higgs. The Casimir eigenvalues of the spin-0 and spin-1 sectors fix the mass ratio through the quartic coupling λ.
proof idea
The declaration is a direct definition that inserts the golden ratio φ into the closed-form expression (3 - φ)/6.
why it matters
This definition is invoked by the HiggsRungCert structure and by mH_prediction_in_interval, which establishes that the RS Higgs mass lies in (120, 130) GeV and contains the observed 125.2 GeV. It also supports the WeinbergAngleScoreCardCert that certifies agreement with the experimental sin²θ_W band. In the framework it realizes the link between the eight-tick octave of the Q₃ group and the electroweak mixing angle, consistent with the forced constants c = 1, ħ = φ^{-5} and the alpha inverse band.
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