sin2ThetaW_GUT
plain-language theorem explainer
The definition fixes the GUT-scale value of sin²θ_W at exactly 3/8, the canonical SU(5) unification prediction. Electroweak unification researchers would cite it when matching Recognition Science running predictions against the observed 0.23 at the Z pole. It is introduced by direct constant assignment with no computation or auxiliary lemmas.
Claim. The GUT-scale value of sin²(θ_W) is defined as 3/8.
background
The module derives the weak mixing angle from the 8-tick phase geometry of Recognition Science, where electroweak mixing arises as an embedding constrained by φ optimization. The Weinberg angle parametrizes the relative strengths of electromagnetic and weak forces, with the target low-scale value sin²(θ_W) ≈ 0.2229 at M_Z. Upstream results supply collision-free empirical programs and algebraic tautologies that underwrite the placement of such constants without new axioms.
proof idea
Direct definition that assigns the constant 3/8. No lemmas or tactics are invoked; the declaration serves as the base input for the running-angle function and the GUT-prediction theorem in the same module.
why it matters
This supplies the fixed GUT input for the gut_prediction theorem and the runningAngle definition. It encodes the SU(5) value at ~10¹⁶ GeV that the Recognition Science framework runs down the φ-ladder to recover the observed low-scale angle, linking directly to the eight-tick octave and the alpha band. The module doc-comment flags the result as part of the PRL paper on electroweak mixing from information-theoretic principles.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.