Finsler Geometric Formulation of Entanglement-Driven Cosmological Expansion Paper XXV

We demonstrate that the Entanglement-Driven Cosmological Expansion (EDCE) framework developed in Papers I--XXIV possesses a natural geometric formulation within Finsler geometry. By constructing a velocity-dependent metric from the one-particle distribution function (1PDF) of entropy-generating astrophysical processes (stellar nucleosynthesis and black hole accretion), we derive a Finsler-Friedmann equation whose predictions are mathematically equivalent to the EDCE Governor equation. This geometric unification reveals that the phantom dark energy equation of state w(t) arises naturally from the anisotropic velocity structure encoded in the 1PDF, providing a geometric interpretation of entanglement-driven expansion. We validate the equivalence numerically across cosmic history (0.5 < t < 14.4 Gyr) and achieve correlation r > 0.95 with RMS difference ∆w