  The goal of this paper is twofold. First, we give a simple proof that
sufficiently sparse Navier--Stokes solutions do not develop singularities. This
provides an alternative to the approach of \cite{Grujic2013}, which is based on
analyticity and the `harmonic measure maximum principle'. Second, we analyze
the claims in \cite{algebraicreduction,grujic2019asymptotic} that \emph{a
priori} estimates on the sparseness of the vorticity and higher velocity
derivatives reduce the 'scaling gap' in the regularity problem.
