The no-fragmentation criterion for plateaux in the expanded quantum infinite well

Let $N$ be the parameter appearing in the expanded quantum infinite well, let $\Lambda\in\mathbb{Q}$, and assume that there is no fragmentation. A plateau is a plateau of the probability distribution studied in the paper. No-fragmentation plateau conjecture. There exists a plateau if and only if $2N\Lambda$ is an odd integer. Moreover, the plateau is unique. The preceding discussion says that this is suggested by computer simulations and would cover all cases in which plateaux appear for rational $\Lambda$; its status is not resolved in the supplied text.