The existence conjecture for elliptic canonical bases

Let ${\mathfrak{X}}$ be the symplectic-resolution object under consideration, and let $\Xi_{{\mathfrak{X}}}$ be the parameter set for elliptic canonical-basis classes. Let Properties A, B, C, D, and E denote the holomorphicity, $K$-theory-limit, duality, $q$-difference, and $v$-difference properties stated in the paper. Elliptic canonical-basis existence conjecture. There exist classes ${\mathcal{E}}^{ell}_{{\mathfrak{X}}}(\mu)$ for every $\mu\in\Xi_{{\mathfrak{X}}}$ satisfying Properties A, B, C, D, and E. These properties are motivated by explicit toric hyper-Kähler examples, but their simultaneous existence is not proved in the supplied text.