MSFCM Paper V: The Origin of the Four-Quadrant Jet–Filament Alignment Structure — Accretion Geometry, Initial Spin Orientation, and the Kinetic–Gravitational Transition at vᵢnf = 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 fₚerp = σ³/ (σ³+vᵢnf³) and the initial alignment signal ⟨cos2δ⟩ᵢnit = (vᵢnf³−σ³) / (vᵢnf³+σ³) are derived analytically from BHL accretion in two channels of the NFW filament potential. The kinetic–gravitational transition condition vᵢnf (ρₜhresh) =σ defines ρₜhresh 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.