K-theoretic lace diagram formula for type A quiver orbit closures

Let $T$ be a maximal torus in $G$, let $\mu$ be an orbit of representations of an arbitrary quiver of type $A$, and let $\overline{\mu}$ denote its closure. A K-theoretic lace diagram for $\mu$ is a lace diagram obtained from a minimal lace diagram representing $\mu$ by the specified transformations. For such a diagram ${\mathbf w}$, let $\mathfrak G({\mathbf w})$ be the Laurent polynomial obtained from the lace-diagram Schubert-polynomial expression by replacing each Schubert polynomial with the corresponding Grothendieck Laurent polynomial. Write $d(\mu)$ for the codimension of the orbit and $\ell({\mathbf w})$ for the length of the lace diagram. K-theoretic lace diagram formula. The $T$-equivariant Grothendieck class of $\overline{\mu}$ is

$$[\mathcal O_{\overline{\mu}}]=\sum_{\mathbf w}(-1)^{\ell(\mathbf w)-d(\mu)}\mathfrak G(\mathbf w),$$

where the sum is over all K-theoretic lace diagrams for $\mu$. This conjecture extends the component formula for quiver orbit closures and the K-theoretic component formula known for equioriented type A quivers to arbitrary orientations.