Bondal–Polishchuk transitivity conjecture for full exceptional sequences

Let $\mathcal{T}$ be a triangulated category admitting a full exceptional sequence of length $n$, and let $\mathfrak{B}_n$ denote the braid group on $n$ strands. The group $\mathbb{Z}^n\rtimes\mathfrak{B}_n$ acts on the set of full exceptional sequences in $\mathcal{T}$. Bondal–Polishchuk conjecture. The action of $\mathbb{Z}^n\rtimes\mathfrak{B}_n$ is transitive on the set of full exceptional sequences in $\mathcal{T}$. This conjecture concerns the classification of full exceptional sequences up to shifts and braid-group mutations. It has been proved for the derived category of a gentle algebra arising from a dissection of a marked surface with zero genus, while the paper provides counterexamples in other settings.