The Tor generator conjecture for Cohen–Macaulay quotients

Let $(R,m)$ be a regular local ring with Krull dimension $n$. Suppose $I+J$ is an $m$-primary ideal in $R$ and $R/I$ and $R/J$ are Cohen–Macaulay. The Tor generator conjecture. The module $\operatorname{Tor}_1(R/I,R/J)$ needs at least $\operatorname{ht}(I)+\operatorname{ht}(J)-n$ generators. In particular, if $I$ and $J$ are two $m$-primary ideals, then $\operatorname{Tor}_1(R/I,R/J)$ needs at least $n$ generators. This conjecture motivates the study of the minimal number of generators of first Koszul homology over Artinian local rings. The source provides no resolution status.