Gluing conjecture for relative Seiberg–Witten invariants

Let $X_1$ be a cobordism between three-manifolds $Y_1$ and $Y_2$, and let $X_2$ be a cobordism between $Y_2$ and $Y_3$. Denote by $\mathcal{D}_{X_1}$, $\mathcal{D}_{X_2}$, and $\mathcal{D}_{X_1 \cup X_2}$ the morphisms associated with these cobordisms in the Seiberg–Witten–Floer stable homotopy category. Gluing conjecture. The morphism associated with the composite cobordism satisfies

$$\mathcal{D}_{X_1 \cup X_2} \cong \mathcal{D}_{X_2} \circ \mathcal{D}_{X_1}.$$

This is the expected functoriality or gluing law for the relative Seiberg–Witten invariant under composition of cobordisms. The supplied text gives no evidence that the statement has been proved or disproved.