MSFCM Paper VI: Velocity Field Anisotropy in Cosmic Filaments — The Q₂₂ Tensor as the Physical Origin of the Four-Quadrant Jet–Filament Alignment Flip

We demonstrate analytically that the NFW virial identity forces v_inf/σ_eff = constant for any velocity scaling, ruling out potential-geometric mechanisms as the origin of the four-quadrant flip detected in Paper IV. We resolve this by direct measurement of the gas velocity field anisotropy from LoTSS DR2 × Tempel 2014 (N=80,695 pairs). The second-order alignment tensor Q₂₂(ρ,r⊥) ≡ ⟨cos2δ⟩ changes sign at ρ_thresh=2.09 and is independent of r⊥ across [0,3] Mpc, confirming a bulk anisotropy of the filament gas velocity field. The excess of perpendicular orientations in Q3 relative to Q1 is Δf⊥=+0.0975, detected at p=7×10⁻⁶⁹ (KS) and p=2×10⁻²⁴⁵ (χ²). Prediction for Paper VII: M_BH ∝ σ⁴_fil, testable with JWST at z>7.