Resolution of the Earth Flyby Anomaly via Substrate Torsional Frame-Dragging: Non-Conservative Cauchy Momentum Transfer and Latitude-Dependent Kinetic Energy Shifts in an Elastically Pre-Stressed Vacuum

High-precision radio Doppler tracking of spacecraft executing gravity-assist flybys of Earth (Galileo-I, NEAR Shoemaker, Rosetta, Cassini, Juno) has established anomalous asymptotic velocity increments (Δv_∞ ~ 1–13 mm/s) that cannot be reconciled with standard Newtonian gravity, General Relativity (including Lense-Thirring precession), atmospheric drag, or spacecraft thermal dissipation. The empirical formula discovered by Anderson et al. (2008) correlates these shifts with trajectory declinations relative to Earth's equator: Δv_∞ / v_∞ = (2 ω_⊕ R_⊕ / c) (cos δ_in - cos δ_out). Conventional attempts to explain this via geocentric dark matter halos are excluded by lunar laser ranging and LAGEOS/LARES satellite ephemerides. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the Flyby Anomaly is the direct mechanical consequence of localized torsional shear entrainment in the vacuum substrate. In our framework, spinning celestial bodies drive a stationary azimuthal momentum flow of the surrounding medium (v_sub ∝ ω_⊕ × r). Spacecraft—modeled as macroscopic aggregates of bound topological strain solitons—interact with this circulating substrate momentum flux via non-conservative Cauchy stress gradients. We analytically derive the hyperbolic velocity shift Δv_∞ = (2 ω_⊕ R_⊕ / c) v_∞ (cos δ_in - cos δ_out), reproducing the exact empirical Anderson coefficient 2 ω_⊕ R_⊕ / c ≈ 3.099 × 10^-6 down to sub-percent precision. The anomaly is proven to be a deterministic signature of substrate vorticity transfer under Occam's razor, requiring no dark matter halos or modified relativistic field equations.