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 d_c = 7 (from Adams' theorem on parallelizable spheres) as an information saturation scale. Four beyond-GR predictions are derived: (1) dark energy w_0 = -6/7 (0.35 sigma from DESI DR2); (2) gravitational wave echoes at tau = r_s/(pi c); (3) a scale-dependent Hubble parameter H_eff = H_0(1 + delta/d_c^2); and (4) CMB cosmic birefringence beta = 0.29 degrees from information-geometric torsion, consistent with ACT DR6 and Planck 2018 detections. The Weinberg angle sin^2(theta_W) = 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 d_c = 7 is shared with companion papers on fermion mixing (chi^2 = 2.63), Koide corrections, dark energy, and neutrino masses, providing cross-domain unity.