The cohomological-weight and Grothendieck-Teichmüller isomorphism conjecture

Let $A(M^{\delta}_0)$ be the cooperadic algebra associated with Brown's compactified moduli spaces, let $\mathsf{coGer}$ be the coGerstenhaber cooperad, and let $\boldsymbol{\mathcal{Z}}_{\scriptstyle{\mathrm{ns}}}$ denote the associated algebra construction. Write $Q$ for the indecomposable quotient and $\mathfrak{grt}_1'$ for the graded dual of the Grothendieck-Teichmüller Lie algebra. Cohomological-weight isomorphism conjecture. There are isomorphisms

$$Q\boldsymbol{\mathcal{Z}}_{\scriptstyle{\mathrm{ns}}}(A(M^{\delta}_0))\cong Q\boldsymbol{\mathcal{Z}}_{\scriptstyle{\mathrm{ns}}}(\mathsf{coGer})\cong \mathfrak{grt}_1'\oplus\mathbb{Q}x^{01}.$$

This would identify the indecomposable formal weights from the moduli-space model with those from the coGerstenhaber model and with the Grothendieck-Teichmüller Lie algebra together with the weight-two generator. Its status is not resolved in the supplied text.