Five-part orbit conjecture for symplectic finite models

Let $e\in\mathfrak{sp}_{2n}$ be a nilpotent element whose partition has five parts, and let $S_e$ be the set of centrally extended orbits generated by the good multiplication rules described in the source. Let $Y_e$ be the associated finite model. Five-part orbit conjecture. The centrally extended orbits that appear in $Y_e$ are precisely the orbits in the set $S_e$. The claim proposes a complete combinatorial description of the orbit types in the five-part symplectic case; the supplied passage gives no resolution.