The analytic spread bound for ideals in Noetherian local rings

Let $(R,\mathfrak{m},k)$ be a Noetherian local ring and let $I$ be an ideal of $R$. Write $\operatorname{s\ell}(I)$ for the symbolic analytic spread of $I$.

Symbolic analytic spread conjecture. One has

$$\operatorname{s\ell}(I)\leq \dim R.$$

This conjecture proposes that symbolic analytic spread is bounded above by the dimension of the ambient Noetherian local ring. The source presents it as an open question, and no resolution is given in the supplied text.