  We reveal a novel mathematical structure in physical observables, the mass of
tachyon fluctuation mode and the energy density, associated with a classical
solution of vacuum string field theory constructed previously [hep-th/0108150].
We find that they are expressed in terms of quantities which apparently vanish
identically due to twist even-odd degeneracy of eigenvalues of a Neumann
coefficient matrix defining the three-string interactions. However, they can
give non-vanishing values because of the breakdown of the degeneracy at the
edge of the eigenvalue distribution. We also present a general prescription of
correctly simplifying the expressions of these observables. Numerical
calculation of the energy density following our prescription indicates that the
present classical solution represents the configuration of two D25-branes.
