The orientifold Hodge equality conjecture

Let $Q$ be a $\sigma$-symmetric quiver. For $e\in\Lambda_Q^{\sigma,+}$, let $W^{\mathsf{prim}}_{Q,e}$ be the primitive orientifold Donaldson–Thomas contribution, let $\mathfrak{M}_e^{\sigma,\mathsf{st}}$ be the moduli scheme of stable self-dual representations, and let $PH^{\bullet}(\mathfrak{M}_e^{\sigma,\mathsf{st}})$ denote the pure part of its cohomology. Write $\mathcal{E}(e)$ for the grading shift appearing in the construction.

Orientifold Hodge equality conjecture. The canonical surjection

$$W^{\mathsf{prim}}_{Q,e}\twoheadrightarrow PH^{\bullet}(\mathfrak{M}_e^{\sigma,\mathsf{st}})\{\mathcal{E}(e)/2\}$$

is an isomorphism.

This predicts that the primitive orientifold Donaldson–Thomas contribution is exactly the pure cohomology of the stable self-dual moduli space, with the indicated grading shift. The supplied text gives no resolution status.