  We construct a class of BRST-invariant closed string states for any classical
solution of open string field theory. The closed string state is a nonlinear
functional of the open string field and changes by a BRST-exact term under a
gauge transformation of the solution. As a result, its contraction with an
on-shell closed string state provides a gauge-invariant observable of open
string field theory. Unlike previously known observables, however, the
contraction with off-shell closed string states in the Fock space is well
defined and regular. Moreover, we claim that the BRST-invariant closed string
state coincides, up to a possible BRST-exact term, with the boundary state of
the boundary conformal field theory which the solution is expected to describe.
Our construction requires a choice of a propagator strip. If we choose the
Schnabl propagator strip, the BRST-invariant state becomes explicitly
calculable. We calculate it for various known analytic solutions of open string
field theory and, remarkably, we find that it precisely coincides with the
boundary state without any additional BRST-exact term. Our results imply, in
particular, that the wildly oscillatory rolling tachyon solution of open string
field theory actually describes the regular closed string physics studied by
Sen using the boundary state.
