Djament's isomorphism conjecture for the wheeled PROP of stable cohomology

Let $\mathcal{E}$ and $\mathcal{H}$ be the wheeled PROPs in the paper, and let

$$\varphi:\mathcal{E}\to\mathcal{H}$$

be the morphism of wheeled PROPs whose image is isomorphic to $\mathcal{K}$. Djament's conjecture. The morphism $\varphi$ is an isomorphism of wheeled PROPs. This reformulates Djament's conjecture that the natural maps from the relevant Ext-groups to stable cohomology are graded isomorphisms, compatibly with PROP compositions and contractions.