Emergent Gravity from Finite Information Density in Bounded Systems

Title: Gravity as an Emergent Limit of Information: Curvature from Bekenstein Bounds and Effective Bit Density Description: This paper presents an information-theoretic model in which gravitational curvature emerges from finite informational bounds. Using only gravitational mass as input, a scalar–tensor mapping is constructed that yields an emergent radius from a system’s bit capacity, without requiring spatial or acceleration data as priors. The core relation is rooted in a re-expression of the Bekenstein bound, modulated by a fixed 67% rendering fraction interpreted as gravitationally effective information. The model is empirically validated across a wide spectrum of physical systems, including planets, stars, compact objects, black holes, and galaxies. For each class, model-derived radii closely match observed values, confirming the viability of the mapping. A taxonomy of mass plateaus (67/x) is introduced to characterize distinct informational regimes, with denominators x \in \{45, 15, 1\} reflecting stable coupling states. The work proposes a fundamentally informational basis for gravitational geometry and opens a new path toward entropic interpretations of spacetime without assuming the Einstein field equations or geometric curvature as axiomatic. A detailed thermodynamic derivation of the rendering constant is deferred to future work.