Yu's conjecture on the degree of the Jacobian bracket

Let $k[x_1,\ldots,x_n]$ be a polynomial ring, and let $f$ and $g$ be algebraically independent polynomials whose homogeneous components of maximal degree are algebraically dependent. Suppose that $f$ and $g$ generate their respective integral closures $C(f)$ and $C(g)$ in $k[x_1,\ldots,x_n]$, and that neither $\deg f$ divides $\deg g$ nor $\deg g$ divides $\deg f$. Yu's conjecture. Then

$$\deg[f,g]>\min\{\deg(f),\deg(g)\}.$$

This conjecture gives a proposed lower bound for the degree of the bracket under algebraic dependence of the leading homogeneous components and the stated integral-closure hypotheses. The source invokes it in connection with determining multidegrees of tame polynomial automorphisms, but does not provide evidence of a resolution.