 Indeed, if (random) $N \in {{\mathbb N}}$ is such that $\A^{0,H}_n(\Lambda \times G) = \emptyset$ for every $n > N$ almost surely then for every cylinder $C \in \A^{0,H}_N(\Lambda \times G)$ and $\varepsilon \geq 0$ we have that $$C \in \mathcal{K}^\varepsilon \Longleftrightarrow F(C) < 