The least accumulation-point conjecture for permutation-class growth rates

Let $\xi\approx 2.30524$ be the unique positive root of $x^5-2x^4-x^2-x-1$, and let the accumulation points from above of a set of real numbers be limits approached by larger elements of that set. Least accumulation-point conjecture. The least accumulation point from above in the set of growth rates of permutation classes is $\xi$. The preceding proposition shows that the growth rates in $[\xi,\zeta]$, where $\zeta\approx 2.32331$, contain a perfect set and hence that $\xi$ is an accumulation point from above; the conjecture asserts that no smaller such accumulation point exists.