Thomas–Yong's minuscule jeu de taquin rule for K-theoretic Schubert calculus

Let $G/P$ be a minuscule flag variety, let $u/\lambda$ be a skew shape in its associated minuscule poset, and let ${\tt INC}_{G/P}(\nu/\lambda)$ denote the increasing tableaux of that shape. Let $K{\tt rect}_{G/P}$ be K-rectification and $S_\mu$ the superstandard tableau of shape $\mu$. Write $C_{\lambda,\mu}^{\nu}(G/P)$ for the corresponding K-theoretic Schubert structure constant.

Thomas–Yong's conjecture. For any minuscule $G/P$,

$$(-1)^{|\nu|-|\lambda|-|\mu|} C_{\lambda,\mu}^{\nu}(G/P)$$

is equal to the number of $T\in {\tt INC}_{G/P}(\nu/\lambda)$ such that

$$K{\tt rect}_{G/P}(T)=S_\mu.$$

This is a proposed positive combinatorial rule for the K-theoretic Schubert structure constants of all minuscule flag varieties, extending the Grassmannian case. The source gives no resolution status for the conjecture.