The Lagrangian–Poisson correspondence conjecture

Let $f:X\to Y$ be an $n$-shifted Lagrangian morphism, and let $\pi_f$ be the associated $(n-1)$-shifted Poisson structure on $X$. Consider the subspace of such morphisms for which the formal completion map $\widehat{Y}_f\to Y$ is an equivalence.

Lagrangian–Poisson correspondence conjecture. The map $f\mapsto\pi_f$ provides an equivalence between the space of $n$-shifted Lagrangian morphisms $f:X\to Y$ such that $\widehat{Y}_f\to Y$ is an equivalence and the space of $(n-1)$-shifted Poisson structures on $X$ in the sense of Pantev–Toën–Vaquié–Vezzosi.

This conjecture proposes that, under the formal-completion condition, the construction from shifted Lagrangian morphisms to shifted Poisson structures is an equivalence. The source gives no resolution.