prediction1
plain-language theorem explainer
Prediction 1 supplies the initial RS estimate for sin²(θ_W) as one quarter minus one eighth of the golden ratio phi, evaluating to roughly 0.1727. A physicist testing information-theoretic derivations of electroweak parameters against collider measurements would cite this value when ranking the first phi-based mixing angle. The declaration is a direct real-number definition with no lemmas or reductions applied.
Claim. $sin^2(θ_W) = 1/4 - 1/(8φ)$
background
Recognition Science obtains phi as the self-similar fixed point of the J-cost function J(x) = (x + x^{-1})/2 - 1. The module applies 8-tick phase geometry to electroweak mixing, where the Weinberg angle arises from gauge-group embedding optimized by phi. The module document states that this angle fixes the relative strengths of electromagnetic and weak forces with target sin²(θ_W) ≈ 0.2229 at the Z scale.
proof idea
The declaration is a direct definition that evaluates the algebraic expression 1/4 - 1/(8*phi) in the reals using the imported constant phi. No lemmas or tactics are invoked.
why it matters
This definition opens the Weinberg angle sequence in the SM-004 module and instantiates the 8-tick geometry step of the forcing chain. It supplies the first numerical input for the paper proposition on electroweak mixing from information-theoretic principles. Sibling definitions later compare it to observation via bestPrediction.
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