  We illustrate a method for computing the number of physical states of open
string theory at the stable tachyonic vacuum in level truncation approximation.
The method is based on the analysis of the gauge-fixed open string field theory
quadratic action that includes Fadeev-Popov ghost string fields. Computations
up to level 9 in the scalar sector are consistent with Sen's conjecture about
the absence of physical open string states at the tachyonic vacuum. We also
derive a long exact cohomology sequence that relates relative and absolute
cohomologies of the BRS operator at the non-perturbative vacuum. We use this
exact result in conjunction with our numerical findings to conclude that the
higher ghost number non-perturbative BRS cohomologies are non-empty.
