Ben-Zvi's microlocal homology invariance conjecture

Let $X$ be a smooth ambient space, let $f$ define the derived zero locus $\boldsymbol{Z}(f)$, and let $V^{\vee}$ be the ambient dual vector space. The source gives a closed immersion

$$T^*[-1]\boldsymbol{Z}(f)\hookrightarrow Z(f)\times V^{\vee}.$$

For $d4aa,d4aa'\subset V^{\vee}$, define

$$\widetilde{d4aa}:=T^*[-1]\boldsymbol{Z}(f)\cap (Z(f)\timesd4aa).$$

Let $M_{\Lambda}^f$ be the microlocal homology associated to $\Lambda$. Ben-Zvi's invariance conjecture. If $\widetilde{\Lambda}=\widetilde{\Lambda'}$, then

$$M_{\Lambda}^f\simeq M_{\Lambda'}^f.$$

The conjecture says that microlocal homology depends only on the part of the parameter set intersecting the scheme of singularities of $\boldsymbol{Z}(f)$, viewed in the indicated trivial family over $Z(f)$; the source gives no evidence of a proof or disproof.