Equal-maximal-rate poisoning conjecture

Let $n$ and $d$ be arbitrary, and let $p_1,p_2,\ldots,p_n$ denote the type-dependent poisoning parameters of the particle system. Starting from the all-zero configuration, suppose that there are distinct types $i$ and $j$ such that $p_i=p_j$ and every other parameter is no larger. Equal-maximal-rate poisoning conjecture. Under these conditions, the probability of poisoning is $0$. The conjecture strengthens the preceding theorem, which shows that poisoning in states $i$ or $j$ has probability $0$; the remaining assertion concerns poisoning in states with smaller parameters.