The CM Metric: From Clausius-Mossotti to Schwarzschild

V3 UPDATE (12 May 2026): Coordinate labels corrected (photon sphere and ISCO directions in circumferential coordinates). New sections: §4. 6 QPO Correspondence (CM ISCO frequency 1819/M Hz matches observed QPOs within 3-37% for four X-ray binaries with dynamically measured masses, vs 17-232% for Kerr) ; §4. 7 Spin Analysis (CM ISCO nearly spin-independent at ±2% due to gₜt × gᵣr = 1, compared to Kerr which varies 5× with spin). Field equation now available (Singh 2026k). QPO data corrected to primary sources (Strohmayer 2001, Motta 2014). SgrA* distance updated to 8. 277 kpc (GRAVITY 2021). All coordinate-independent predictions unchanged. Original abstract: A static, spherically symmetric spacetime metric derived from the Clausius-Mossotti relation (1879). The CM metric ds² = W^ (1/3) c²dt² - W^ (-1/3) (dr²+r²dΩ²), with W= (1-β²) / (1+2β²) and β²=2GM/ (rc²), reproduces Schwarzschild at 1PN (γ=β=1), passes all 6 classical GR tests, and predicts 10% larger black hole shadows (testable by ngEHT). Zero free parameters.