Automatic Relativistic Corrections from the Clausius-Mossotti W^ (-1/3) Potential: Tested Against Measured Data for Z = 1 to 92

The CM metric's Klein-Gordon equation produces a derived potential V = μ² (W^ (-1/3) − 1), where W = (1−β²) / (1+2β²). This single closed-form function automatically includes relativistic corrections to all orders. Tested against measured 1s binding energies for 23 hydrogen-like ions (Z = 1 to 92): CM beats Coulomb in 21/23 cases. Average error: Coulomb 2. 05%, CM 0. 54%, Dirac 0. 38%. Heavy atoms (Z > 26): Coulomb 4. 5% → CM 1. 1% (4× improvement). Uranium: Coulomb 12. 6% → CM 0. 6% (20× improvement). Five spin correction variants tested — every correction makes it worse, confirming spin-orbit is already included non-perturbatively. CM closes 90% of the Coulomb-to-Dirac accuracy gap. No free parameters. Paper 2026u in the Speed Gap (CM) Framework series.