Weak defectivity of extremal automata

Let $\mathcal{A}=(Q,\Sigma,\delta)$ be an extremal automaton, meaning an automaton whose shortest reset word reaches the relevant extremal bound. An automaton is weakly defective in the sense defined in the paper. Weak-defectivity conjecture for extremal automata. Every extremal automaton is weakly defective.

The conjecture is proposed as a possible route toward proving that every extremal automaton is irreducible. The source says that weak defectivity holds for all known extremal automata, but does not establish it for arbitrary extremal automata.