weak_mixing_phi_based
plain-language theorem explainer
The theorem asserts that the φ-derived best prediction for the weak mixing angle equals (3 - φ)/6. Researchers in beyond-Standard-Model physics and unification schemes would reference this when evaluating geometric origins of SM parameters. The proof reduces to unfolding the relevant prediction definitions and confirming equality by reflexivity.
Claim. $sin^2 θ_w = (3 - φ)/6$, where φ is the golden-ratio fixed point forced by the Recognition Composition Law.
background
Module C-014 derives the three gauge couplings from Recognition Science ledger geometry. Electromagnetic α follows from 4π·11 cube edges plus gap correction; strong α_s equals 2/W with W the wallpaper-group count 17; the weak sector supplies sin²θ_w via φ-structure. The φ-ladder and J-cost enter through upstream phi-forcing results that fix the self-similar constant used in the prediction. The local setting treats the tree-level 3/8 value as the high-scale starting point whose running is approximated by the low-energy φ expression.
proof idea
The proof is a one-line wrapper that unfolds bestPrediction and prediction3, then applies reflexivity.
why it matters
This supplies the explicit φ-based entry for sin²θ_w inside the C-014 gauge-coupling registry. It feeds the unification hint by giving a low-energy anchor that evolves toward the GUT-scale convergence of α, α_s and α_w. The result closes the structural-origin subsection of the derivation chain and touches the open question of how the φ-ladder supplies the precise running correction between tree level and M_Z.
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