A Dynamical OE Lagrangian: From Clausius-Mossotti to Orbital Mechanics

We extend the static Lagrangian L = OE - W (Singh 2026h) to a dynamical Lagrangian by separating inside (OE, kinetic) from outside (1/W, potential):

L_dyn = T_OE(v) + V/W(r) = ½mv²/(1+2β²) - GMm/(r×W_field)

with two independent β values (particle velocity, field strength). Results: (i) Newton's F=ma recovered exactly; (ii) angular momentum and energy conserved to 10⁻¹⁴; (iii) Mercury precession = -4/3 × GR exactly at all eccentricities; (iv) V/W contributes +2 × GR universally; (v) total = +2/3 × GR with zero fitted parameters = virial compression fraction; (vi) GR decomposed as 4π (sphere, CM spatial) + 2π (circle, temporal); (vii) Bohr-Sommerfeld action S = p_θ × 2π = nh verified for hydrogen. The framework derives 2/3 of GR from 145-year-old electromagnetic medium physics, universally from atoms to planets.