HγC VI: Self-Selection of Coarse-Graining Regimes in Relational Accumulation Gravity

In relational approaches to emergent gravity, macroscopic gravitational behavior can arise from the accumulation of microscopic relational updates. In previous work within the relational accumulation framework, an effective accumulation field was introduced to describe how retained relational structure influences large-scale dynamics after coarse-graining. However, the physical status of the coarse-graining parameter governing this process has remained unclear. In this work we propose that the coarse-graining parameter should not be regarded as an arbitrary external smoothing scale but as a dynamically realized regime descriptor. We introduce a minimal dynamical model in which two competing effects constrain the coarse-graining regime: excessive smoothing suppresses accumulated relational differentiation, while insufficient coarse-graining exposes fluctuating microscopic structure and destabilizes mesoscopic dynamics. The balance between these mechanisms leads to the emergence of a preferred regime toward which the system dynamically organizes. This self-selection mechanism naturally produces a near-critical accumulation regime in which the response of the accumulation field becomes maximally effective. Within this regime, the relation between baryonic structure and effective gravitational acceleration exhibits a characteristic scaling behavior consistent with the observed radial acceleration relation in galaxies. In this interpretation, the radial acceleration relation arises not as a fundamental modification of gravitational laws but as a manifestation of near-critical accumulation dynamics. These results suggest that galactic gravitational phenomenology may reflect the statistical organization of coarse-graining regimes in relational accumulation processes.