  Using the new approach to analytic geometry developed by Clausen and Scholze
by means of condensed mathematics, we prove that for every affinoid analytic
adic space $X$, pseudocoherent complexes, perfect complexes, and finite
projective modules over $\mathcal{O}_X(X)$ form a stack with respect to the
analytic topology on $X$; in particular, we prove that the category of vector
bundles on $X$ is equivalent to the category of finite projective modules over
$\mathcal{O}_X(X)$. To that end, we construct a fully faithful functor from the
category of complete Huber pairs to the category of analytic rings in the sense
of Clausen and Scholze and study its basic properties. Specifically, we give an
explicit description of the functor of measures of the analytic ring associated
to a complete Huber pair. We also introduce, following the ideas of
Kedlaya-Liu, notions of \textit{pseudocoherent module} and
\textit{pseudocoherent sheaf} in the context of adic spaces (where the latter
can be regarded as an analogue of the notion of coherent sheaf in algebraic
geometry) and show that there is a similar equivalence of the corresponding
categories.
