Conjecture on decreasing limiting missing-difference distributions

Let $R_n$ be the random set used in the paper, and let $f_{[0,n-1]}^-(R_n”)$ denote the number of missing differences in the interval $[0,n-1]$ for the corresponding random model. For each integer $m\geq 0$, consider the limiting probability

$$\lim\limits_{n \to \infty} P\left[f_{[0,n-1]}^-(R_n”)=m\right].$$

Decreasing limiting-distribution conjecture. For all integers $m\geq 0$, this limiting function of $m$ is decreasing.

The conjecture is motivated by the observed decreasing trend of the finite distributions after their tail-end blip becomes negligible. The source provides numerical evidence but no proof or resolution.