  Let $f: X \to \mathbb{A}^1$ be a regular function on a smooth complex
algebraic variety $X$. We formulate and prove an equivalence between the
algebraic formal twisted de Rham complex of $f$ and the vanishing cycles with
respect to $f$ as objects in the category of sheaves valued in the derived
$\infty$-category of modules over
$\widehat{\mathscr{E}}_{\mathbb{C},0}^{\mathrm{alg}}$, the ring of germs of
algebraic formal microdifferential operators. This is a direct generalization
of Kontsevich's conjecture, proven in work by Sabbah and then Sabbah--Saito, of
an algebraic formula computing vanishing cohomology.
  The novelty in our approach is the introduction of a canonical $V$-filtration
on the derived $\infty$-category of regular holonomic
$\mathscr{D}_{\mathbb{C},0}$-modules, and the use of various techniques from
the theory of higher categories and higher algebra in the context of the
subject of microdifferential calculus.
