To close this critical gap, we propose here a definition of e c (r) based on the MPAC framework, which provides a formal ground for pointwise mapping of the HF density to E c . We achieve this by developing a general strategy for constructing correlation energy density gauges, from which both our new definition of e c (r) and DFT's e DFT c (r) within the conventional gauge (see above) naturally emerge. In this way, our definition of e c (r) provides a wavefunction-based E c analog of DFT's conventional gauge e DFT c (r). As we shall show later, despite belonging to two distinct frameworks, these two objects share several key features.