3 problems

Schubert-cell perfect-basis conjecture. For every $w\in W$, the coordinate algebra $\mathbb{C}[X_w^\vee]$ has a perfect basis.

Saturated-valuation conjecture. Under these assumptions, such a strongly positive unipotent bicrystal exists and the valuation-induced map identifies the normal crystal of…

Perfect-basis realization conjecture. Such a based module and linear map exist.