Causal Memory Gravity IX: UV Completion via Functional Renormalization Group (FRG/EAA)

This paper develops a minimal ultraviolet completion of the memory sector in Causal Memory Gravity (CMG) using the Effective Average Action and the Functional Renormalization Group. Starting from the localized auxiliary-field form of the nonlocal CMG memory term, the work derives beta functions for the running couplings and studies the fixed-point structure of the theory. The main result is that the memory mass ratio behaves as a UV-relevant direction, while the memory amplitude becomes UV-irrelevant in the minimal truncation. In this way, the paper places CMG into an asymptotic-safety-style renormalization framework while preserving its distinctive infrared memory signature. The work provides the UV bridge between the effective infrared CMG description and a more fundamental renormalization-group completion.