Vanishing of Hochster's theta pairing on even-dimensional isolated hypersurfaces

Let $R$ be an admissible hypersurface, meaning that $\widehat{R}$ is a quotient of an unramified or equicharacteristic regular local ring by a nonzero element, with an isolated singularity. Assume that $\dim R$ is even. For $R$-modules $M$ and $N$, if

$$\operatorname{Tor}_i^R(M,N)=0$$

for some $i$, then

$$\operatorname{Tor}_j^R(M,N)=0$$

for all $j\geq i$. This is the expected consequence of the conjectural vanishing of Hochster's theta pairing $\theta^R(M,N)$ for even-dimensional isolated hypersurfaces.