HγC V: From Relational State Transitions to the Relational Accumulation Field: A Microscopic Foundation for Emergent Gravity

We develop a microscopic relational foundation for the accumulation field A(x) in the HγC framework. The underlying substrate is described as an event-based relational network whose fundamental processes are local relational state transitions ordered by a pre-temporal relational update parameter τ. Each admissible transition contributes a retained weighted trace, so that microscopic accumulated history is defined not by event count alone, but by the ordered accumulation of non-erased relational imprints embedded in the evolving substrate. We show that, after coarse-graining over suitable relational neighborhoods and update windows, these accumulated traces admit a smooth mesoscopic representation identified…