V.R306 — The sqrt3

The factor sqrt(3) = |1 - omega| where omega = e^(2 pi i/3) appears in three independent contexts: the mass ratio correction sqrt(3) iota_tau^(-2) in R, the proton-neutron mass difference delta_A/m_n approx (sqrt(3)/2) iota_tau^6, and the closing identity alpha_G = alpha^18 sqrt(3)(1 - (3/pi)alpha). All three arise from three-fold lemniscate crossing symmetry.