The shifted cotangent polyvector-field conjecture

Let $X$ be an Artin stack and let $n$ be an integer. The shifted cotangent stack $\boldsymbol{T}^*[n]X$ has a canonical $n$-shifted symplectic structure, and its functions identify with the graded commutative algebra

$$\Gamma\big(X,S(\mathbb{T}_X[-n])\big).$$

Polyvector-field conjecture. The resulting $\mathbb{P}_{n+1}^{gr}$-algebra structure on $\Gamma\big(X,S(\mathbb{T}_X[-n])\big)$ is equivalent to the $\mathbb{P}_{n+1}^{gr}$-algebra $\mathbf{Pol}(X,n)$ of $n$-shifted polyvector fields from Pantev–Toën–Vaquié–Vezzosi.

This conjecture identifies the Poisson algebra induced by the shifted symplectic structure on a shifted cotangent stack with the intrinsic algebra of shifted polyvector fields. Its resolution is not supplied in the source.