Information-Driven Gravity: Tensor Completion, Ghost-Freedom, and Euclid Predictions (Synthesis)

Synthesis paper presenting the complete Information-Driven Gravity (IDG) program across Papers I–VIII. Covers: Wilsonian RG derivation of the scalar action, the scalar trilemma and its tensor resolution, ghost-freedom via two independent proofs (Fisher-Rao kinematic argument + determinant lower bound theorem), the exact geometric identity f_aniso = 1/4, gravitational slip prediction η_IDG(k,z) = 1 − A(z)·k²/(k²+m_s²) with η < 1, Euclid detectability analysis (SNR = 1.0 at β = 0.1, SNR = 3.83 at β = 0.2), proof that Tensor IDG lies outside the Horndeski class via three independent arguments, and a first-principles derivation of the Fisher-Rao identification via the Chentsov-Amari uniqueness theorem. Falsifiability window: Euclid/DESI/Rubin 2028–2035. [Version 8 (July 2026): Retypeset in LaTeX. Formatting revision only — no changes to content, derivations, results, or figures.]