Finite-projective-dimension decency conjecture

Let $R$ be a local ring and let $M$ be an $R$-module of finite projective dimension. For every $R$-module $N$ such that $l(M\otimes_RN)<\infty$, finite-projective-dimension decency conjecture. One has

$$\dim M+\dim N\leq\dim R.$$

This is the decency assertion discussed among the homological conjectures in the source. The provided text does not state a resolution status for this formulation.