Generic period conjecture for crystal cellular automata

Let $p\in P(m)$ be a state with soliton content $m$, and let $(T^{(r)}_l)^t(p)\neq0$ for every $t\geq0$. Denote by ${\mathcal P}^{(r)}_l$ the least common multiple defined earlier in the source. Generic period conjecture. The dynamical period of $p$ under $T^{(r)}_l$, namely the minimum positive integer $t$ such that $(T^{(r)}_l)^t(p)=p$, equals ${\mathcal P}^{(r)}_l$ generically and is a divisor of ${\mathcal P}^{(r)}_l$ otherwise. This gives the expected generic orbit length of a state in terms of the Bethe-ansatz period formula; exceptional states may have shorter periods. The supplied text gives no resolution status.