  Let $X$ be a smooth algebraic variety over $k$. We prove that any flat
quasicoherent sheaf on $\operatorname{Ran}(X)$ canonically acquires a D-module
structure. In addition, we prove that, if the geometric fiber
$X_{\overline{k}}$ is connected and admits a smooth compactification, then any
line bundle on $S \times \operatorname{Ran}(X)$ is pulled back from $S$, for
any locally Noetherian $k$-scheme $S$. Both theorems rely on a family of
results which state that the (partial) limit of an $n$-excisive functor defined
on the category of pointed finite sets is trivial.
