The d-algebra structure conjecture for translation-dilation invariant QFTs

Let $V=\mathbb{R}^d$, let $\Phi$ be the bundle of local fields of a quantum field theory, and let $\Phi_0$ be its fiber at the origin. Let $G_d$ be the group of parallel translations and dilatations. A $d$-algebra is an algebra over the chains on the little $d$-discs operad. The $d$-algebra structure conjecture for QFTs. For any QFT on $V$ invariant under $G_d$, in particular for any conformal field theory, the tensor product

$$\Phi_0\otimes\wedge^*(V^*)$$

has a structure of a $d$-algebra. The source presents this as plausible and gives no proof; it connects the conjecture to homotopy Lie algebras governing translation-invariant deformations of QFTs.