Observables for identity-based tachyon vacuum solutions

We consider a modified KBc algebra in bosonic open string field theory expanded around identity-based scalar solutions. By use of the algebra, classical solutions on the background are constructed and observables for them, including energy densities and gauge invariant overlaps, are calculable. These results are applied to evaluate observables analytically for both of the identity-based trivial pure gauge solution and the identity-based tachyon vacuum solution.