  We construct massive open string states around a classical solution in the
oscillator formulation of Vacuum String Field Theory. In order for the correct
mass spectrum to be reproduced, the projection operators onto the modes of the
left- and right-half of the string must have an anomalous eigenvalue 1/2, and
the massive states are constructed using the corresponding eigenvector. We
analyze numerically the projection operators by regularizing them to finite
size matrices and confirm that they indeed have eigenvalue 1/2. Beside the
desired massive states, we have spurious massive as well as massless states,
which are infinitely degenerate. We show that these unwanted states can be
gauged away.
