Smoothability of noncollapsed RCD(−2,3) 3‑manifolds into Ricci limits

Ascertain whether every noncollapsed RCD(−2,3) metric space (X^3,d) that is a topological 3‑manifold is a noncollapsed three-dimensional Ricci limit space.

Background

The authors establish manifold recognition for certain 3D RCD spaces but note that the broader smoothability question—whether such spaces arise as Ricci limit spaces—is completely open. This parallels long‑standing open problems in Alexandrov geometry regarding smoothability.

A resolution would bridge synthetic lower Ricci curvature theory and classical geometric analysis by confirming that topological 3‑manifold RCD structures can be approximated by smooth manifolds with lower Ricci and volume bounds.