The paper is organized as follows. In Sec. II, we provide the necessary theoretical background for this work. Sec. III introduces our general correlation energy density gauge strategy, from which our new MPAC-based e c (r) naturally arises (derived in Sec. IV). In Sec. V, we leverage our full configuration interaction (FCI) implementation along the MPAC to present highly accurate e c (r) for small atoms and diatomics. Finally, in the concluding section VI, we emphasize the importance of our newly defined e c (r) in establishing a solid foundation for both traditional functionals (e.g., local MPAC-based interpolations) and ML-driven approximations that map HF-density-based features to E c .