prediction4
plain-language theorem explainer
This definition supplies the candidate expression 1 - 3/(4φ) for sin²(θ_W) in Recognition Science units. An electroweak phenomenologist would cite it when scanning the set of φ-derived mixing angles against the measured 0.2229. The definition is a direct arithmetic evaluation of the golden-ratio constant imported from the eight-tick geometry.
Claim. The candidate value for the squared sine of the Weinberg angle is given by $1 - 3/(4φ)$, where $φ$ is the golden-ratio fixed point of the Recognition Composition Law.
background
The module derives the Weinberg angle from the 8-tick phase geometry of Recognition Science, in which electroweak mixing arises as an embedding angle constrained by φ optimization. The target observable is sin²(θ_W) ≈ 0.2229 at the Z scale, which fixes the relative strengths of the electromagnetic and weak forces. Upstream, the structure as from ContinuumBridge equates the discrete Laplacian action on simplices to a weighted sum of defects, supplying the geometric substrate for the mixing parameter.
proof idea
The declaration is a direct noncomputable definition that evaluates the arithmetic expression 1 - 3/(4*phi) using the imported constant φ. No lemmas or tactics are invoked beyond the module imports.
why it matters
It forms one of the five explicit predictions for sin²(θ_W) inside the SM-004 derivation of electroweak mixing from information-theoretic principles. The expression connects to the eight-tick octave landmark and the paper proposition on φ-constrained gauge embeddings. Although the numerical result 0.536 is flagged as too large, the definition contributes to the candidate pool examined by sibling selectors such as bestPrediction.
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