MSFCM Paper V: The Origin of the Four-Quadrant Jet–Filament Alignment Structure — Accretion Geometry, Initial Spin Orientation, and the Kinetic–Gravitational Transition at v_inf = σ

We derive the physical origin of the four-quadrant alignment structure detected in Paper IV (LoTSS DR2, N=80,695 pairs). The radial accretion fraction f_perp = σ³/(σ³+v_inf³) and the initial alignment signal ⟨cos2δ⟩_init = (v_inf³−σ³)/(v_inf³+σ³) are derived analytically from BHL accretion in two channels of the NFW filament potential. The kinetic–gravitational transition condition v_inf(ρ_thresh)=σ defines ρ_thresh with no free parameters. The complete evolution equation reproduces all four quadrants of Paper IV with a single calibrated amplitude A0. Relativistic corrections (Kerr–Schild, MPD, geodetic) are 5–18 orders of magnitude below the BHL torque at filament scales.