  It is known that a closed collapsed Riemannian $n$-manifold $(M,g)$ of
bounded Ricci curvature and Reifenberg local covering geometry admits a
nilpotent structure in the sense of Cheeger-Fukaya-Gromov with respect to a
smoothed metric $g(t)$. We prove that a canonical nilpotent structure over a
regular limit space that describes the collapsing of original metric $g$ can be
defined and uniquely determined up to a conjugation, and prove that the
nilpotent structures arising from nearby metrics $g_\epsilon$ with respect to
$g_\epsilon$'s sectional curvature bound are equivalent to the canonical one.
