The remainder vanishing conjecture for Jacobian pairs

Let

$$\mathcal{Q}=\{(a,b,m,n)\in\mathbb{Z}_{>0}^4:m<n,\ a\mid m,\ a\mid n,\ \gcd(a,b)=1,\ 2\leq a<b\}.$$

For $F\in\mathbb{C}[x,y]$, let $N^0(F)$ be its augmented Newton polygon, let $T_{m,n}$ be the corresponding trapezoid, and let $F_i^{(0,1)}$ and $F_i^{(1,1)}$ denote its homogeneous components for the indicated gradings. Suppose $(a,b,m,n)\in\mathcal{Q}$ and $F,G\in\mathbb{C}[x,y]$ satisfy the five conditions in the conjecture: the specified trapezoidal supports for $F$ and $G$, the $(x+1)$- and $(x+y)$-divisibility conditions on the components of $F$, and $[F,G]\in\mathbb{C}$.

The remainder vanishing conjecture. Under these conditions,

$$[F,G]=0.$$

The paper names this conjecture and states that it implies the Newton-polygon criterion, hence the two-dimensional Jacobian conjecture. Its resolution status is not supplied in the source material.