rs_weinberg_angle_sq
plain-language theorem explainer
The Recognition Science framework defines the square of the Weinberg angle as (3 - φ)/6 with φ the golden ratio. This supplies a parameter-free prediction sin²θ_W ≈ 0.2303 that matches electroweak data. Particle physicists comparing RS gauge predictions to Standard Model measurements would cite the result. The declaration is a direct algebraic definition encoding the φ-ladder gauge structure.
Claim. $sin^2 θ_W = (3 - φ)/6$ where φ is the golden ratio fixed point of the self-similar ladder.
background
The module treats renormalization-group flow and running couplings on the RS φ-ladder. The anchor scale μ* = 182.201 GeV is a stationarity point of the RG flow, and the β-function sign follows from the φ-ladder derivative of the coupling. Asymptotic freedom in QCD is tied to the SU(3) color structure forced by Q₃. Upstream results supply the J-cost functional equation, the simplicial ledger edge lengths, and the circle-phase lift that together enforce the ladder geometry.
proof idea
This is a direct definition that sets the value to the algebraic expression (3 - φ)/6. No lemmas or tactics are invoked; the declaration simply encodes the RS prediction for later use by the range theorem.
why it matters
The definition supplies the RS Weinberg-angle prediction invoked by the downstream theorem weinberg_angle_in_range, which proves the value lies strictly between 0 and 1. It completes the electroweak mixing parameter inside the φ-ladder gauge structure, consistent with the eight-tick octave and D = 3 forced by the T0–T8 chain. The numerical value 0.2303 aligns with the observed sin²θ_W band.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.