  Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic
generic fiber $X$. We obtain a global equivalence between the category
$\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational
Hodge--Tate crystals on the absolute prismatic site $(\frakX)_{\Prism}$ and the
category $\HIG^{\nil}_*(X)$ of enhanced Higgs bundles on $X$. Along the way, we
construct an inverse Simpson functor from $\HIG^{\nil}_*(X)$ to the category
$\Vect(X_{\proet},\widehat\calO_X)$ of generalised representations on $X$,
which turns out to be fully faithful.
