The Moore–Piepmeyer–Spiroff–Walker eta-pairing conjecture for complete intersections

Let $R$ be a local ring which is an isolated singularity, meaning that $R_{\mathfrak p}$ is a regular local ring for every non-maximal prime ideal $\mathfrak p$ of $R$. Let $M$ and $N$ be finitely generated $R$-modules. For a complete intersection, $\eta^R_c(M,N)$ denotes the eta-pairing in codimension $c$.

Moore–Piepmeyer–Spiroff–Walker conjecture. If $R$ is a complete intersection of codimension $c\geq 2$, then

$$\eta^R_{c}(M,N)=0$$

for all finitely generated $R$-modules $M$ and $N$.

This conjecture concerns vanishing of the highest potentially nonzero eta-pairing and is attributed in the source to Moore, Piepmeyer, Spiroff, and Walker. The supplied text gives no evidence of a resolution.