Intersection-dimension conjecture for even-dimensional admissible hypersurfaces

Let $R$ be an admissible hypersurface with an isolated singularity, and let $M,N$ be $R$-modules such that the tensor product has finite length:

$$\ell(M\otimes_R N)<\infty.$$

Intersection-dimension conjecture. If $\dim R$ is even, then

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

The statement is described as a consequence of the preceding theta-vanishing conjecture and is an intersection-theoretic dimension inequality for modules over hypersurfaces. The source does not state whether it has been resolved.