Information-Driven Gravity VIII: Tensor IDG — Ghost-Freedom, Anisotropic Gravitational Slip, and Euclid Predictions

We present Tensor IDG, the resolution to the scalar IDG trilemma identified in Paper VII. Promoting the scalar field φ to a rank-2 symmetric tensor Φ_μν identified with the Fisher-Rao information metric, we demonstrate that the tensor Klein-Gordon equation □Φ_μν − mₛ²Φ_μν = (β/MPl) T_μν simultaneously satisfies the S8 tension, CMB energy density bounds, and anisotropic chameleon screening — the three constraints the scalar theory could not jointly satisfy. We prove ghost-freedom via two independent arguments: (1) a kinematic argument showing the Fisher-Rao identification enforces det (Φ) > 0 as a covariance identity, and (2) an explicit lower bound theorem det (Φ (t) ) ≥ det (Φ₀) ·exp (−C·t²). We prove Tensor IDG lies outside the Horndeski class via three independent proofs: opposite sign of gravitational slip, violation of the (μ−1) (η−1) ≥ 0 consistency relation, and an anisotropic slip tensor with no scalar-tensor analog. The anisotropy factor fₐniso = 1/4 is an exact geometric identity, mass and concentration independent. The falsifiable Euclid prediction is ηIDG (k, z) = 1 − A (z) ·k²/ (k²+mₛ²) with η < 1, detectable at SNR = 1. 0–3. 83 for β = 0. 1–0. 2. The Kähler geometry of the IDG statistical manifold fixes cFR = 1/ (16π²), leaving exactly two free parameters: mₛ and β.