  We study ghost number one excitations on the sliver to investigate the
solution of string field actions around the tachyon vacuum. The generalized
gluing and resmoothing theorem is used to develop a method for evaluating the
effective action for excitations on both the wedge states and the sliver state.
We analyze the discrete symmetries of the resulting effective action for
excitations on the sliver. The gauge unfixed effective action till level two
excitations on the sliver is evaluated. This is done for the case with the BRST
operator $c_0$ and $c_0 + (c_2 + c_{-2})/2$ with excitations purely in the
ghost sector. We find that the values of the effective potential at the local
maximum lie close by for the zeroth and the second level of approximation. This
indicates that level truncation in string field theory around the tachyon
vacuum using excitations on the sliver converges for both choices of the BRST
operator. It also provides evidence for the conjectured string field theory
actions around the tachyon vacuum.
