Time as Phase Flow III: Information-Geometric Backreaction and the Microscopic Origin of Temporal Inertia

The standard cosmological model (ΛCDM) faces persistent challenges from the H₀ and S₈ tensions, alongside anomalies in early galaxy formation. In this work, we present a first-principles derivation of Information-Geometric Spacetime (IGS) dynamics within a unified action framework incorporating holographic backreaction. Treating the universe as an open quantum system in the Schwinger–Keldysh (in-in) formalism, we derive an effective temporal constitutive relation in which the conventional time evolution is replaced by a state-dependent phase response, suppressed by entanglement entropy. This deformation manifests as a modified time–energy commutation structure governed by an information-geometric coupling β. We show that β is not a phenomenological parameter, but a universal geometric quantity fixed by the causal-diamond structure in (3+1) dimensions, yielding β ≈ 0.1837. The resulting dynamics imply an emergent information-induced friction and a redshift-dependent effective cosmological constant, leading to a percent-level suppression of late-time structure growth and providing a unified explanation of the S₈ tension and early massive galaxy formation.