Universality conjecture for the final particle count

Let $N\geq 1$ be the initial number of particles, and let $\tilde{X}_N$ denote the random number of particles remaining after the perfectly plastic collision process. A random variable is universal here if its distribution does not depend on the initial velocity distribution. Universality conjecture. For $N\geq 1$, $\tilde{X}_N$ is universal. This conjecture is motivated by simulations using ten different initial velocity distributions, which found no statistically significant distributional differences; its validity beyond the studied cases remains open.