The epi-morphism kernel generator conjecture

Let $k$ be a field of characteristic zero, and let

$$\varphi:k[X_1,X_2,\ldots,X_n]\longrightarrow k[Y_1,\ldots,Y_m]$$

be an epimorphism of $k$-algebras. Set $I=\ker(\varphi)$, and let $\mu(I)$ denote the minimal number of generators of $I$. Epi-morphism kernel generator conjecture. One should have

$$\mu(I)=n-m.$$

This is presented as a weaker version of the epi-morphism problem attributed to S. Abhayankar, which asks for a stronger coordinate-generation statement. The supplied text does not give a resolution of this weaker conjecture, although it records its connection with Murthy's conjecture.