Duality conjecture for ideal access structures

Let $\mathcal A$ be an access structure. It is ideal if it can be realized by an ideal entropic polymatroid, equivalently by an ideal distribution scheme. Let $\mathcal A^\bot$ denote the dual access structure. Duality conjecture for ideal structures. The dual of an ideal access structure is ideal.

This is a particular case of the broader conjecture that entropic complexity is invariant under duality. The source says that this special case had resisted all efforts and that refuting it does not necessarily refute the broader conjecture, since the dual might be non-ideal while having complexity $1$. The parser marks this conjecture as disproved.