The $L_{\infty}$ and $d$-algebra structure conjecture for CFT deformations

Let ${\cal A}$ be the cooperad governing the OPE data, let $H$ be the state space regarded as an ${\cal A}$-algebra, and let $\mathfrak g$ be the $L_{\infty}$-algebra controlling formal deformations of $H$ as an ${\cal A}$-algebra. Define

$$\Omega^d(H)=H\otimes\wedge^d(\mathbb R^d).$$

An $L_{\infty}$-morphism is a morphism in the homotopy Lie-algebraic sense, and a $d$-algebra is the structure referenced in [KoSo2]. $L_{\infty}$ and $d$-algebra structure conjecture. There is an $L_{\infty}$-algebra structure on $\Omega^d(H)$, there exists an $L_{\infty}$-morphism $\Omega^d(H)\to\mathfrak g$, and there is a $d$-algebra structure on $\Omega^{\bullet}(H)$. The conjecture proposes algebraic structures on the differential-form-valued CFT state space and a map to its deformation-controlling algebra; the source gives no resolution.