Vasconcelos's conjecture on vanishing first Hilbert coefficients

Let $A$ be a Noetherian local ring with maximal ideal $\mathfrak m$ and positive dimension $d=\operatorname{dim} A$. For an $\mathfrak m$-primary ideal $I$, write $e_1(I)$ for the first Hilbert coefficient defined by the Hilbert–Samuel polynomial, and call $Q$ a parameter ideal if it is generated by a system of parameters. Call $A$ unmixed when $\operatorname{dim} \widehat{A}/\mathfrak p=d$ for every $\mathfrak p\in\operatorname{Ass}(\widehat{A})$, where $\widehat{A}$ is the $\mathfrak m$-adic completion of $A$.

Vasconcelos's conjecture. Assume that $A$ is unmixed. Then $A$ is a Cohen–Macaulay local ring once $e_1(Q)=0$ for some parameter ideal $Q$ of $A$.

The conjecture concerns whether the vanishing of the first Hilbert coefficient detects Cohen–Macaulayness under the unmixedness hypothesis. The paper's abstract states that this conjecture is solved affirmatively; the supplied statement is therefore a theorem rather than an open conjecture.