Gravitational Surface Redshift from the CM Metric: An EOS-Independent Test, Coordinate Corrections, and Interior Field Equation

The Clausius-Mossotti (CM) metric ds² = W^ (1/3) c²dt² − W^ (−1/3) (dr²+r²dΩ²), where W = (1−β²) / (1+2β²) and β² = 2GM/ (rc²), reproduces all six classical tests of general relativity at 1PN order (Singh 2026j). This paper reports three developments. First, a coordinate correction: the CM photon sphere is 34% further from the horizon than GR in circumferential coordinates (not 5. 7% closer as stated in 2026j), and the ISCO is 10. 3% further. All coordinate-independent observables — shadow (+10. 0%), ISCO frequency (−17. 2%), binding energy (−4. 7%) — remain unchanged. Second, an EOS-independent surface redshift prediction: zCM = W^ (−1/6) − 1, differing from GR by 28–37% for NICER pulsars. For J0740+6620, the Iron Kα line is predicted at 5. 10 keV (CM) vs 4. 57 keV (GR) — a 540 eV gap detectable with XRISM. Third, the correct Euler-Lagrange equation from the CM action, with matter coupling δSₘ/δΦ = − (ε+P). Zero freely adjustable parameters. 9 chapters, 15 references.