Folklore conjecture on Ricci-flow singularity models

A gradient shrinking soliton is a Riemannian manifold $(M,g)$ equipped with a function $f\in C^\infty(M)$ satisfying

$$\operatorname{Ric}+\nabla^2f-\frac12g=0.$$

Such a soliton generates a self-similar Ricci flow and is invariant under parabolic rescaling. Folklore conjecture. For any Ricci flow, “most” singularity models are gradient shrinking solitons. Gradient shrinking solitons provide natural self-similar blow-up models, and the conjecture is motivated by Hamilton's work and analogous results for mean curvature flow. In the paper, the precise meaning of “most” is deliberately left vague, so the conjecture remains open as stated.