In this work, we study the problem of testing m-\emph{grainedness} of probability distributions over an n-element universe \mathcal{U}, or, equivalently, of whether a probability distribution is induced by a multiset S\subseteq \mathcal{U} of size |S|=m. Recently, Goldreich and Ron (Computational Complexity, 2023) proved that \Omega(n^c) samples are necessary for testing ... more >>>