The equivariant Waldhausen A-theory derivative conjecture

Let $\Gmr$ be a finite group, and let ${\bf B}_{\Gmr}{\bf Top}^{(1)}$ denote the first layer of the equivariant Weiss functor ${\bf B}_{\Gmr}{\bf Top}$. Suppose there exists an incomplete equivariant $\Amr$-theory functor ${\bf A}_{\Gmr}'$ with codomain $\operatorname{\mathcal{S}p}^{\Gmr}_{(1)}$. Equivariant Waldhausen A-theory derivative conjecture. The first derivative at the zero object satisfies

$${\bf \Theta} {\bf B}_{\Gmr}{\bf Top}^{(1)}({\bf 0})\simeq {\bf A}_{\Gmr}'(\ast).$$

This would identify the first derivative of the equivariant topological Weiss functor with an incomplete genuine equivariant Waldhausen $A$-theory of a point, extending the classical nonequivariant calculation. The conjecture is presented as an expectation conditional on the existence of ${\bf A}_{\Gmr}'$, and no resolution is given.