Relaxation-time dependence of post-collision jamiton length

Let $\tau$ be the relaxation time, and consider the jamiton produced by a collision. Denote its length by $L$. Length-dependence conjecture. The length of the jamiton resulting from a collision depends on $\tau$. Numerical observations show that the post-collision length increases as $\tau$ increases, while the source relates this dependence to the length formula; the general claim remains unproved.