Unoriented string-diagram model conjecture

Let $\mathcal{SD}^{\mathrm{u}}$ be the space of unoriented string diagrams, and let $\mathcal{M}$ be the moduli space of Riemann surfaces with parameterized boundary. Unoriented string-diagram model conjecture.

$$\mathcal{SD}^{\mathrm{u}}\simeq\mathcal{M}.$$

This is the unoriented version of the proposed homotopy model for the moduli space used in string topology. The source presents it as a future direction and supplies no evidence that it has been proved.