Terminal-leaf conjecture for the frames of maximal-class p-groups

Let $p\geq 5$ be prime and let $i>p+1$. Let $\mathcal F_i$ be the frame and $\mathcal B_i$ the associated branch of groups of maximal class.

Terminal-leaf conjecture. The leaves of the frame $\mathcal F_i$ are terminal groups in $\mathcal B_i$.

The conjecture concerns the eventual structure of the frames studied computationally for several primes. The paper does not state a resolution, so the terminality assertion remains open.