  Given an integral scheme X over a non-archimedean valued field k , we
construct acuniversal closed embedding of X into a k-scheme equipped with a
model over the field with one element (a generalization of a toric variety). An
embedding into such an ambient space determines a tropicalization of X by
earlier work of the authors, and we show that the set-theoretic tropicalization
of X with respect to this universal embedding is the Berkovich analytification
of X. Moreover, using the scheme-theoretic tropicalization, we obtain a
tropical scheme $Trop_{univ}(X)$ whose T-points give the analytification and
which canonically maps to all other scheme-theoretic tropicalizations of X.
This makes precise the idea that the Berkovich analytification is the universal
tropicalization. When X = spec A is affine, we show that $Trop_{univ}(X)$ is
the limit of the tropicalizations of X with respect to all embeddings in affine
space, thus giving a scheme-theoretic enrichment of a well-known result of
Payne. Finally, we show that $Trop_{univ}(X)$ represents the moduli functor of
semivaluations on X, and when X = spec A is affine there is a universal
semivaluation on A taking values in the idempotent semiring of regular
functions on the universal tropicalization.
