3 problems

Vanishing-of-cascades conjecture. For every $\alpha s\in{\mathscr S}$, the sequence $\left(\kappa_{\alpha s}(n)\right)_n$ tends to $0$ as $n$ tends to infinity. Consequently, $Q$ i…

Geometric convergence conjecture. If the tree has no infinite shift-stable subtree, then all its cascade series converge with geometric rates.

Right-eigenvalue conjecture. If, for every $\alpha s\in{\mathscr S}$, the sequence $\left(\kappa_{\alpha s}(n)\right)_n$ converges to $0$, then $Q$ admits $1$ as a right eigenvalue…