Balanced subgraph counts and quasirandomness: a proof of the Janson--Sós conjecture

Let $F$ be a finite simple graph with $m$ vertices and at least two edges, and let $p\in(0,1]$. We prove that a graph sequence is $p$-quasirandom if and only if the symmetrized counts of copies of $F$ across every balanced partition into $m$ classes have the asymptotics predicted by the random graph