The repeated averages process on a graph works as follows: assign a real number to each node, then repeatedly pick a random edge and replace both endpoint values with their common average. The question is whether this process always undergoes a sharp transition, called a cutoff, where the distribution goes from being far from equilibrium to being very close to it in a very short window of time relative to the total mixing time. The counterexample paper shows that naive conjectures about this mixing time fail, but a complete characterization of when cutoff occurs and what drives the mixing time remains open.