Ben-Zvi's resolution conjecture for microlocal homology

Let $X$ be a smooth space, let $\boldsymbol{Z}(f)$ be the derived zero locus associated to $f$, let $d4aa^f_{\Lambda}$ denote the microlocal homology object associated to $d4aa\subset V^{\vee}$, and let $M_{\Lambda}^f$ be the corresponding complex. Suppose that the regularity conditions are indexed by $d4aa$. Ben-Zvi's conjecture. There should exist a resolution of $M_{\Lambda}^f$ by the pullback of currents on $X$ with prescribed regularities, such as wave front sets contained in a prescribed conic subset of the cotangent bundle, dictated in some way by $d4aa$. This conjecture proposes a current-theoretic model for microlocal homology and would connect its algebraic construction with regularity conditions on currents; no resolution of the asserted kind is established here.