The Koszul resolution conjecture for the basic deformation-quantization bimodule

Let $X$ be a finite-dimensional vector space, let $A=\wedge(X)=\mathrm S(X[-1])$ with generators of degree $1$, and let $B=\mathrm S(X^*)$ concentrated in degree $0$. Let $K$ be the $A_\infty$-$A$-$B$-bimodule whose structure maps include the canonical pairing action described in Proposition 1. The bimodule $K$ is conjecturally quasi-isomorphic to the Koszul free resolution

$$\wedge(X^*)\otimes \mathrm S(X^*)$$

of the right $\mathrm S(X^*)$-module $\mathbb R$, where $\wedge(X)$ acts from the left by contraction.

This would give a direct algebraic description of the basic bimodule arising in the simplest deformation-quantization case, replacing its integral formulas by the standard Koszul model. The source presents this as an expected description; no resolution is established in the supplied text.