Lee–Weinberg–Yi specialization conjecture for monopole metrics

Let $\mu_0\in\mathfrak g$ be nonzero, let $\mu:[0,\delta]\to\mathfrak g$ be a regular deformation of $\mu_0$, meaning that $\mu(t)$ is regular for all $t>0$, and set ${\mathcal M}_t={\mathcal M}(u,\mu_t,k)$ with $g_t$ its $L^2$ metric. Lee–Weinberg–Yi conjecture. Given any nonzero $\mu_0\in\mathfrak g$, there is a regular deformation $\mu_t$ such that

$$({\mathcal M}_t,g_t)\text{ tends to }({\mathcal M}_0,g_0)\text{ as }t\to0.$$

This predicts continuity of the hyperKähler monopole metrics under specialization from regular to possibly singular symmetry breaking; the supplied text presents it as an interesting conjecture.