  We consider "sliver" states which act as projection operators in the matter
star product of Witten's cubic string field theory. These sliver states, which
might be associated with Dirichlet p-branes, are not finite norm states in the
matter string Hilbert space. We describe the singularities of these states, and
demonstrate that the sliver states are composed of strings having singular
geometric features. These singularities take a particularly simple form in the
zero slope limit alpha' -> 0, where the star algebra factorizes into a product
of the algebra of functions on space-time and the noncommutative star product
of fields associated with higher string modes. An analogy to the sliver
geometry suggests a natural mechanism for describing closed string states in
open string field theory.
