Persistence of divots in missing-difference distributions

Let $P_n^{\mathrm{H}}(k)$ denote the probability distribution associated with the relevant diffset statistic, and call $k$ a divot of this distribution when it is a local depression. Let $n_1$ be a positive integer.

Divot persistence conjecture. If $k$ is a divot of $P_{n_1}^{\mathrm{H}}$, then $k$ is also a divot of $P_n^{\mathrm{H}}$ for every $n>n_1$.

This conjecture asserts that once a divot appears, its location never changes as $n$ increases. The source gives no resolution status.