MSFCM Paper IV: Two-Regime Jet–Filament Alignment in LoTSS DR2 and Direct Evidence for Γ_eff ∝ M_BH from a Flux Inversion at S_thresh ≈ 4.77 mJy

First large-scale observational test of the MSFCM using LoTSS DR2 × Tempel 2014 (80,695 AGN–filament pairs). Global signal ⟨cos2δ⟩ = −0.031 at 12.5σ. Two-regime density transition at ρ=2.09 (14.6σ). Flux inversion at S_thresh=4.77 mJy provides direct evidence for Γ_eff ∝ M_BH (Paper II eq. 7), confirmed at Spearman ρ=+0.084 (p<10⁻¹²⁷).