Refined folklore conjecture on Ricci-flow singularity models

A gradient shrinking soliton is a Riemannian manifold $(M,g)$ with a potential function $f$ satisfying

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

A soliton may be degenerate, and its singular set may have codimension at least $4$. Refined folklore conjecture. For any Ricci flow, “most” singularity models are gradient shrinking solitons that may be degenerate and may have a singular set of codimension $\geq4$. This refines the preceding informal conjecture in response to four-dimensional examples whose blow-up models can be singular or degenerate. No resolution is supplied in the source.