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

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... deed 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.