The fractional-support exclusion conjecture

Let $\overline{\mathcal{R}}=\mathbb{C}[x^{1/\mathbf d},y]$ for a fixed positive integer $\mathbf d$, and let $\overline{T}_{m,n,a}$ be the class defined in the paper. Suppose $F,G\in\overline{\mathcal{R}}$ satisfy $[F,G]\in\mathbb{C}\setminus\{0\}$, $F\in\overline{T}_{m,n,a}$, $G\in\overline{T}_{bm/a,bn/a,b}$, and $N^0(F)$ is similar to $N^0(G)$ with the origin as center and ratio $\deg(F):\deg(G)=a:b$. The fractional-support exclusion conjecture. Then

$$\left(\frac{a}{a+b},0\right)\notin N^0(F),\qquad \left(\frac{b}{a+b},0\right)\notin N^0(G).$$

This is part of the paper's proposed analysis of the Jacobian conjecture; no resolution is supplied.