Vasconcelos' uniformity conjecture for Chern coefficients

Let $(R,\mathfrak{m})$ be a Noetherian local ring, let $I$ be an $\mathfrak{m}$-primary ideal, and let $\mathcal{A}$ be an $I$-good filtration. Vasconcelos' uniformity conjecture. There exist functions $f_l(I)$ and $f_u(I)$ defined with extended degree over $R$ such that

$$f_l(I)\leq \mathrm{e}_{1}(\mathcal{A})\leq f_u(I).$$

The conjecture seeks uniform lower and upper bounds for the first Hilbert coefficient of good filtrations in terms of extended degree.