Are (n−3)-symmetric factors Z Ricci limit spaces when n ≥ 4?

Determine whether, for n ≥ 4, any metric space Z appearing as the factor in an (n−3)-symmetric noncollapsed Ricci limit space X = R^{n−3} × Z (as in Theorem 1.7) is itself a noncollapsed three-dimensional Ricci limit space.

Background

Theorem 1.7 shows that if a noncollapsed Ricci limit space splits as X = R^{n−3} × Z in the metric measure sense, then Z is homeomorphic to a topological 3‑manifold. However, beyond the topological classification, it is unclear whether Z also lies in the class of noncollapsed three-dimensional Ricci limit spaces when the ambient dimension n ≥ 4.

Clarifying whether Z is a genuine noncollapsed Ricci limit space would strengthen the structural understanding of (n−3)-symmetric limits and connect the topology of the factor Z to the smooth approximation theory underlying Ricci limit spaces.