MSFCM Paper III: Mathisson–Papapetrou–Dixon Spin–Curvature Coupling in Cosmic Filaments and Observational Predictions for LoTSS DR2

We extend the MSFCM framework to the post-Newtonian relativistic regime using the MPD equations. The dimensionless ratio ε_rel = 4.20×10⁻¹⁸ confirms that the relativistic correction is fully perturbative across the filament regime. Module F7R validates the Paper II tables with ΔC < 10⁻¹³. Primary prediction for LoTSS DR2: the sign of dT₉₀/dσ distinguishes BHL (σ⁴) from the Paper I calibration (σ⁻¹) with SNR ≳ 3.5 for ~5000 sources.