Chapter 27: The Weinberg Angle and CF Encodings

the relevant chapter derived the Weinberg angle from inter-sector coupling: sin²θ_W = ι_τ(1-ι_τ) ≈ 0.2249. This chapter develops the arithmetic of that number. We compute its continued-fraction (CF) expansion, the CF of the W/Z mass ratio cosθ_W, and relate both to the CF structure of the master constant ι_τ itself. Continued fractions reveal the rational approximation hierarchy of a real number—its intrinsic arithmetic skeleton. That the Weinberg angle inherits clean CF structure from ι_τ is evidence that the electroweak mixing angle is not a contingent parameter but a structural consequence of Category τ.