  We call a system super-linearizable if it admits finite-dimensional embedding
as a linear system -- known as a finite-dimensional Koopman embedding; said
otherwise, if its dynamics can be linearized by adding a finite set of
observables. We introduce the notions of visible and hidden observables for
such embeddings which, roughly speaking, are the observables that explicitly
appear in the original system and the ones that do not, but yet are necessary
for its embedding. Distinct embeddings can have different numbers of hidden and
visible observables. In this paper, we derive a tight lower bound for the
number of visible observables of a system among all its super-linearizations.
