Information-Geometric Framework for Gravitational Observables Beyond General Relativity

We present an information-geometric framework that recovers the Einstein field equations (with the standard factor 8 pi G) as a consistency condition via Lovelock uniqueness, then derives observables beyond general relativity. The framework associates a Fisher information metric with the vacuum state and identifies dc = 7 (from Adams' theorem on parallelizable spheres) as an information saturation scale. Four beyond-GR predictions are derived: (1) dark energy w₀ = -6/7 (0. 35 sigma from DESI DR2) ; (2) gravitational wave echoes at tau = rₛ/ (pi c) ; (3) a scale-dependent Hubble parameter Hₑff = H₀ (1 + delta/dc²) ; and (4) CMB cosmic birefringence beta = 0. 29 degrees from information-geometric torsion, consistent with ACT DR6 and Planck 2018 detections. The Weinberg angle sin² (thetaW) = 3/13 at tree level agrees with the PDG value to within one-loop SM radiative corrections. Detection timelines and falsification criteria are presented for current and next-generation experiments. The central parameter dc = 7 is shared with companion papers on fermion mixing (chi² = 2. 63), Koide corrections, dark energy, and neutrino masses, providing cross-domain unity.