Ross–Yong conjecture for Grothendieck polynomials

Let $w\in S_n$ and $\gamma\in\mathbb{Z}_{\geq 0}^n$. Write $g_{w,\gamma}=\#\{P\in {\sf Pipes}(w)\mid {\tt wt}(P)=\gamma\}$, and let ${{\sf KKoh}}(w,\gamma)$ be the set of diagrams obtainable from the diagram $D(w)$ by successive Kohnert and K-Kohnert moves, with weight $\gamma$. Ross–Yong conjecture. The equality

$$g_{w,\gamma}=\#{{\sf KKoh}}(w,\gamma)$$

holds. The conjecture proposed a diagrammatic rule for Grothendieck polynomials; it is false, as shown by the counterexample in this paper.