The orientifold primitive-cohomology conjecture

Let $Q$ be a $\sigma$-symmetric quiver. For a dimension vector $e$, 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 $\mathcal{E}(e)$ be the grading shift. Denote by $PH^{\bullet-\mathcal{E}(e)}(\mathfrak{M}_e^{\sigma,\mathsf{st}})$ the correspondingly shifted pure cohomology.

Orientifold primitive-cohomology conjecture. The surjection

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

is an isomorphism.

The conjecture is motivated by the difficulty of adapting the Nakajima-quiver-variety proof of injectivity to the self-dual setting. The supplied text gives no resolution status.