The nonlinear harmonic bundle conjecture for relative nonabelian Hodge moduli

Let $\alpha_S$ be the canonical homeomorphism between the relative de Rham and Higgs moduli spaces, and assume that it is an isomorphism of differentiable fiber bundles. Denote the resulting differentiable fiber bundle by $\alpha:Z\to S$. Also assume that a Hitchin metric $\omega_H$ as in the relative Hitchin metric gluing conjecture exists, and let $\beta:T_{Z_{\mathbb R}}\cong T_{Z_{\mathbb R}}$ be a suitably defined real tangent-bundle isomorphism. Nonlinear harmonic bundle conjecture. The metric $\omega_H$ is a harmonic metric on $\alpha$ with respect to $\beta$, and consequently $(f,\nabla_{GM};g,\theta_{KS})$ is a nonlinear harmonic bundle over $S$. This is conditional on the differentiable identification and the existence of the global Hitchin metric, and the supplied text gives no evidence that the resulting assertion has been resolved.