The hypothesis is the shallow-minor definition of the nowhere dense concept; the conclusion is the shared predicate $HasSubpolynomialWcol$ of the coloring-number concept. The notes state the bound for the members of the class only, whereas the predicate used here demands it uniformly for all subgraphs of members; the two are equivalent, because the subgraphs of the members of a nowhere dense class again form a nowhere dense class, and the subgraph-uniform form is what downstream localization arguments consume. This is the headline of the submission and is the composition of the four preceding theorem concepts: subpolynomial shallow-minor density, the admissibility bound, and the two links of the coloring-number chain.