sin2ThetaW_predicted
plain-language theorem explainer
Recognition Science supplies the explicit prediction sin²θ_W = 1/(2φ + 1) for the squared Weinberg angle. Electroweak phenomenologists cite it when testing the eight-tick phase embedding of SU(2) × U(1) against the measured value near 0.223. The definition is realized as a direct arithmetic substitution of the golden ratio constant.
Claim. The predicted value of the squared Weinberg angle is given by $1/(2φ + 1)$, where $φ$ is the golden ratio fixed point arising from the self-similar structure in the forcing chain.
background
The module derives W and Z boson masses from φ-quantized gauge structure. Observed values satisfy m_W/m_Z ≈ 0.8815, which equals cos θ_W by definition, while sin²θ_W is measured near 0.223. Recognition Science constrains the mixing angle through the 8-tick phase geometry: the phases form a Z₈ group into which SU(2) × U(1) embeds, with the embedding angle fixed by φ to yield the stated closed form.
proof idea
The declaration is a direct definition that substitutes the golden ratio into the arithmetic expression 1/(2φ + 1). No lemmas or tactics are invoked; the body encodes the closed-form result obtained from the Z₈ embedding constraint.
why it matters
This definition supplies the concrete RS prediction for sin²θ_W that enters the electroweak mixing analysis and the W/Z mass ratio. It realizes the paper proposition on electroweak parameters from RS and connects directly to the T7 eight-tick octave landmark. The documented 6% discrepancy with observation remains an open question for possible higher-order corrections within the framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.