4 problems

Twig periodicity conjecture. There exist integers $e=e(p)$ and $f=f(p)$ with $(p-1)\mid f$ such that, for every $i\geq e$ and every $\gamma\in\hat{H}_i$,

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

Nontriviality conjecture. For every such $p$, $i$, and $\gamma$,

Twin conjecture. There exists $n_0=n_0(p)$ such that for all $n\geqslant n_0$ and each group $G$ at depth $n-c$ in $\mathcal B_p(n+d)$, there exists a twin $H$ at depth $n-c-d$ in…