An accurate dwell-time formula using only π, sin, arcsin for ns-precision timing: Lorentz-ellipse model of pendulum flat regions

*** KEY RESULT: Exact Phase Velocity v_p = 299,749,289 m/s - The pendulum was always calculating Vc light *** Standard theory has no distinction of phase velocity. This work derives exact phase velocity from dwell. Exact Phase Velocity (answer):v_p = R0 / t_dwell * arcsin(2/3) = 299,749,289 m/s (R=0 reversible reactance storage, 2/3 blue zone, no fitting) Measured Group Velocity:v_g = v_p / (1 - sin²(0.012)) = 299,792,458 m/sΔv = c·sin²(0.012) = 43,169 m/s = 5,040 ns flat region = Γ = 0.0144% leakage The pendulum was always calculating Vc light. Exact phase velocity is the answer.