Simpson-type completeness conjecture for quiver-variety descending manifolds

Let $\mathfrak M_{(0,-2i\zeta_{\mathbb{R}})}$ be the indicated quiver-variety moduli space, let $p_0$ be a fixed point of the $\mathbb{C}^{\star}$-action, and let $W^1(p_0)$ be the intersection of the descending set of $p_0$ with $\mathfrak M_{(0,-2i\zeta_{\mathbb{R}})}$. Quiver-variety completeness conjecture. The submanifold $W^1(p_0)$ is complete in $\mathfrak M_{(0,-2i\zeta_{\mathbb{R}})}$ for every fixed point $p_0$. This is formulated as an analogue of Simpson's conjecture for quiver varieties, following the preceding conformal-limit construction that identifies the relevant descending manifolds.