SNP conjecture for Grothendieck polynomials

For $w\in S_\infty$, let ${\mathfrak G}_w$ be the Grothendieck polynomial obtained recursively using $\overline\pi_i(f)=\partial_i((1-x_{i+1})f)$. A polynomial has SNP when every lattice point of its Newton polytope is an exponent vector. Grothendieck-polynomial SNP conjecture.

$${\mathfrak G}_w\text{ has SNP}.$$

The conjecture was exhaustively checked for $n\leq7$ and generalizes the Schubert SNP conjecture, but remains open in general.