Ross–Yong's K-theoretic Kohnert rule for Grothendieck polynomials

For a permutation $w\in S_n$, let $\mathfrak{G}_w$ be the Grothendieck polynomial, let ${\sf KKoh}(w)$ be the family of $K$-Kohnert diagrams generated from the diagram of $w$, and let $\mathrm{wt}(E)$ be the weight of a diagram $E$. For $\alpha\in\mathbb{Z}_{\geq 0}^n$, write ${\sf KKoh}(w,\alpha)$ for the diagrams of weight $\alpha$ and $\mathrm{PD}(w,\alpha)$ for pipe dreams of weight $\alpha$.

Ross–Yong's Grothendieck-polynomial conjecture. For every permutation $w\in S_n$,

$$\mathfrak{G}_w=\sum_{E\in{\sf KKoh}(w)}(-1)^{|\mathrm{wt}(E)|-\ell(w)}x^{\mathrm{wt}(E)}.$$

Equivalently,

$$\#{\sf KKoh}(w,\alpha)=\#\mathrm{PD}(w,\alpha)\quad\text{for every }\alpha\in\mathbb{Z}_{\geq 0}^n.$$

Robichaux disproved this rule, including an explicit counterexample in $S_8$; hence the conjecture is refuted.