From Discrete Information to Closed 4D Tidal Gravity: Exact 1/9 Tidal Structure and Variational Selection

This paper develops a closed effective 4D gravitational sector from a discrete information-theoretic critical structure. Starting from a microscopic critical tail motivated by Information Causality, the construction proceeds through a one-sided primitive and an effective radial closure to obtain a macroscopic potential with two key features: a Newtonian monopolar term and a tidal correction with exact relative coefficient 1/9. Within this framework, the same microscopic critical tail controls both the leading monopole scale and the first subleading tidal contribution. The resulting effective geometry is then analyzed at the level of metric closure, Einstein tensor structure, weak-field observables, and shadow corrections. In addition, the paper introduces a minimal variational sector that selects an interior phenomenologically admissible branch for the effective parameter governing the 4D family. The scope of the work is deliberately narrow and explicit. The paper does not claim a complete ultraviolet theory of gravity or a first-principles derivation of the absolute observed mass spectrum. Its central claim is instead that a discrete critical information-theoretic structure can generate a consistent effective 4D sector in which the functional monopole scale and the exact relative tidal coefficient emerge in a unified way, with observational consistency in the weak-field and shadow regimes.