The relative Hitchin metric gluing conjecture

Let $S$ be a smooth complex curve, let $X\to S$ be a polarized smooth family of smooth projective curves of genus at least $2$, and let $g:M^{s}_{Hig}(X/S,r)\to S$ be the relative moduli space of rank-$r$ stable Higgs bundles of degree zero, equipped with its relative Higgs field $\theta_{KS}$. For each fiber $Y_s$, let the Hitchin metric mean the fiberwise $L^2$ metric induced by harmonic metrics. Hitchin metric gluing conjecture. There is a hermitian metric $\omega_H$ on $g$, unique up to adding the pullback of a closed two-form on $S$, which is $\theta_{KS}$-adapted and whose restriction to each fiber $Y_s$ is a Hitchin metric. The claim concerns globalizing the fiberwise hyperkähler metrics over the family; the supplied text gives no evidence that this has been resolved.