  The goal of this paper is to show a (derived) $p$-adic Simpson correspondence
for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our
results depend on a deformation to $\mathbf{B}_\mathtt{dr}^+/\xi^2$, and not on
a choice of exponential (as required for more general coefficients). Our
methods are inherently higher categorical, hinging on the theory of modules
over $\mathbf{E}_\infty$-algebras.
