Exceptional-collection conjecture for rational homogeneous spaces

Let $\mathrm{G}$ be a semisimple algebraic group and let $\mathrm{P}\subset \mathrm{G}$ be a parabolic subgroup. Let ${\mathbf D^{\mathrm{b}}}(\mathrm{G}/\mathrm{P})$ denote the bounded derived category of coherent sheaves on $\mathrm{G}/\mathrm{P}$. Exceptional-collection conjecture. The category ${\mathbf D^{\mathrm{b}}}(\mathrm{G}/\mathrm{P})$ has a full exceptional collection. This conjecture is closely related to generic semisimplicity of big quantum cohomology through Dubrovin's conjecture. The source cites substantial progress but does not state that the conjecture is settled in all cases.