We propose a generalization of K-theory to operator systems. Motivated by spectral truncations of
noncommutative spaces described by C*-algebras and inspired by the realization of the K-theory of a
C*-algebra as the Witt group of hermitian forms, we introduce new operator system invariants indexed
by the corresponding matrix size. A direct system is constructed whose direct limit possesses a
semigroup structure, and we define the K0-group as the corresponding Grothendieck group. This is an
invariant of unital operator systems, and, more generally, an invariant up to Morita equivalence of
operator systems. For C*-algebras it reduces to the usual definition. We illustrate our invariant by
means of the spectral localizer