  In a series of papers, Bamler [Bam20a,Bam20b,Bam20c] further developed the
high-dimensional theory of Hamilton's Ricci flow to include new monotonicity
formulas, a completely general compactness theorem, and a long-sought partial
regularity theory analogous to Cheeger--Colding theory. In this paper we give
an application of his theory to lower bounds for the scalar curvatures of
singularity models for Ricci flow. In the case of $4$-dimensional
non-Ricci-flat steady soliton singularity models, we obtain as a consequence a
quadratic decay lower bound for the scalar curvature.
