3 problems

Conjecture. These gradings exhaust the list of fine gradings, up to equivalence, on $\mathfrak{e}_6$, $\mathfrak{e}_7$, and $\mathfrak{e}_8$, with the exception of the root space d…

Exhaustiveness conjecture. The list exhausts the fine gradings, up to equivalence, on $\mathfrak{e}_6$, and it also exhausts them for $\mathfrak{e}_7$ and $\mathfrak{e}_8$.

Normalizer conjugacy conjecture. If $q_1,q_2\in Q$, then they are conjugated in $\mathcal{G}$ if and only if they are conjugated in the normalizer of $Q$.