Perverse-equivalence conjecture for quantum-cohomology eigenlines

Let $A$ be an alcove in the space of real stabilities, and let $\mathcal{E}(A)$ be the set of joint eigenlines for quantum multiplication by equivariant cohomology classes of $Y$ on $H^\bullet_T(Y)$, with quantum parameter in $A$. Perverse-equivalence conjecture. There is a natural indexing of $\mathcal{E}(A)$ by the simple objects of the abelian category, or heart of the $t$-structure, corresponding to $A$, such that monodromy along paths crossing the boundary divisor transversely is given by the permutations of simple objects determined by the corresponding perverse equivalence. This conjecturally identifies quantum-cohomology monodromy with the wall-crossing behavior of hearts of $t$-structures; no proof or resolution is supplied in the source.