Gravity at the Information Limit: The Relativistic Information-State Manifold

Author’s Note: This preprint presents the foundational conceptual architecture and phenomeno-logical mapping of the RISM framework. While the scalar-tensor embedding is mathematically covari-ant, specific geometric derivations are currently framed as heuristic postulates. Rigorous bottom-upderivations and numerical integration of the screening hand-offs are under active development forsubsequent versions.The persistent success of Modified Newtonian Dynamics (MOND) in parametrizing galactic kine-matics suggests a fundamental acceleration threshold, a0, below which standard General Relativitybreaks down. However, theoretical formalizations of this threshold have historically relied on phe-nomenological curve-fitting, and classical scalar-field extensions typically violate multi-messengerspeed constraints (cgw = c). In this paper, we present the Relativistic Information-State Manifold(RISM) framework, which postulates that 4D continuous spacetime acts as an emergent EffectiveField Theory resulting from the coarse-graining of discrete quantum microstates along a 5D entropicresolution axis. By equating the local Unruh temperature of an accelerating frame with the globalGibbons-Hawking temperature of the apparent Hubble horizon, we derive a0 = cH0/2π strictly fromthe thermodynamic periodicity of causal horizons. Treating the vacuum as a constrained Gaussianthermal bath, we demonstrate that the MOND interpolation function naturally emerges as the ex-act Wiener filter response (Free Energy minimization) to competing geometric and cosmic entropygradients. By mapping this informational vacuum strictly onto the shift-symmetric L2 K-essenceand L3 Cubic Galileon sectors of Horndeski gravity, we construct a uniquely integrable ArcsinhK-essence action. This framework cleanly recovers the foundational AQUAL field equations. Whilepure conformal coupling serves as a viable matter-sector approximation, extending the frameworkvia DHOST disformal couplings correctly preserves null geodesics for gravitational lensing. Further-more, by invoking thermodynamic trace-decoupling (T = 0) and shift-symmetric Hubble friction,the framework natively protects standard ΛCDM expansion during the radiation-dominated era,dynamically awakening only at matter-radiation equality to assist in generating the CMB acousticpeaks and late-universe galactic halos.