Extremality of the automata $\mathcal{E}_n$, $\mathcal{E}'_n$, $\mathcal{O}_n$ and $\mathcal{O}'_n$ in the family $\mathcal{A}_{ij}$

Let $\mathcal{E}_n$, $\mathcal{E}'_n$, $\mathcal{O}_n$ and $\mathcal{O}'_n$ be the explicitly constructed automata in the paper, and let $\{\mathcal{A}_{ij}\}_{i\neq j}$ be the indicated family of automata. Extremality conjecture. The automaton $\mathcal{E}_n$ has reset threshold $(n^2-2)/2$, $\mathcal{E}'_n$ has reset threshold $(n^2-10)/2$, and $\mathcal{O}_n$ and $\mathcal{O}'_n$ have reset threshold $(n^2-1)/2$. Furthermore, they represent the automata with the largest possible reset threshold among the family $\{\mathcal{A}_{ij}\}_{i\neq j}$ for, respectively, $n=4k$, $n=4k+2$, $n=4k+1$ and $n=4k+3$. The claim records the reset thresholds and extremal members of this constructed family; the supplied excerpt does not identify a resolution status or provide enough surrounding definitions to assess it independently.