Affine Grothendieck polynomial conjecture for positroid varieties

Let $\Pi_f\subseteq\mathrm{Gr}(k,n)$ be a positroid variety, and let $\tilde{G}_f$ be the affine stable Grothendieck polynomial associated with its affine permutation $f$. Identify $K^*(\mathrm{Gr}(k,n))$ with a ring of symmetric functions as in the cited reference.

Affine Grothendieck polynomial conjecture. The $K$-theory class of the structure sheaf of $\Pi_f$ is the image of $\tilde{G}_f$ under this identification:

$$[\mathcal O_{\Pi_f}]=\tilde{G}_f.$$

This is the $K$-theoretic analogue of the affine Stanley-function description of positroid-variety cohomology classes. The source presents the assertion as a conjecture and gives no resolution.