models is impractical. A more promising alternative is to try to classify those models that are generic, or at least stable. A singularity model developing from certain original data is labeled *stable* if flows starting from all sufficiently small perturbations of that data develop singularities with the same singularity model; it is labeled *generic* if flows that start from an open dense subset of all possible initial data develop singularities having the same singularity model. Clearly, a singularity model can be generic only if it is stable

Important work of Colding and Minicozzi (see [@CM12] and [@CM15]) provides strong support in favor of the conjecture that the only generic singularities of Mean Curvature Flow are generalized cylinders ${\mathbb}R^m\times{\mathcal}S^{n-m}$. Although no analogous result is currently known for Ricci flow, a conjectural picture comes from the work of Cao, Hamilton, and Ilmanen [@CHI04], who define the *central density* $\Theta$ and the *entropy* $\nu({\mathcal}M)$ of a shrinking Ricci soliton ${\mathcal}M$, using Perelman’s reduced volume and entropy, respectively (see [@Pe]). They observe that their central density imposes a partial order on shrinking solitons: monotonicity of the $\nu$-functional in time means that if perturbations of a shrinking soliton develop singularities, these cannot be modeled on 