HγC IV: Emergent Gravity from Relational Accumulation: Coarse-Graining, Near-Criticality, and the Radial Acceleration Relation

We propose a minimal effective framework for emergent gravity in which gravitational acceleration is generated by spatial gradients of a coarse-grained accumulation field A(x) sourced by baryonic matter. The field A(x) represents the cumulative organization of relational structure at an effective level and provides a macroscopic description of how baryonic distributions constrain gravitational response. This effective formulation builds on the broader history-based relational framework and on the regime-level role of coarse-graining developed in earlier work. Within this framework, the radial acceleration relation observed in galaxies can be interpreted as the manifestation of a near-critical response regime of the accumulation field rather than as a fundamental modification of the gravitational law. The characteristic acceleration scale a0 then acquires a natural interpretation as a cosmologically normalized scale associated with the large-scale organization of accumulated structure, while residual scatter in the relation may reflect fluctuations of the coarse-grained field. These results suggest that some galactic gravitational phenomena commonly attributed either to modified gravity or to dark matter may instead arise as emergent properties of accumulated relational structure. The present paper develops the minimal effective-theory foundation of this framework; its microscopic origin, dynamical regime structure, and broader cosmological extensions are left to subsequent work.