  Assuming that around the tachyon vacuum the kinetic term of cubic open string
field theory is made purely of ghost operators we are led to gauge invariant
actions which manifestly implement the absence of open string dynamics around
this vacuum. We test this proposal by showing the existence of lump solutions
of arbitrary codimension in this string field theory. The key ingredients in
this analysis are certain assumptions about the analyticity properties of
tachyon Green's functions. With the help of some further assumptions about the
properties of these Green's functions, we also calculate the ratios of tensions
of lump solutions of different dimensions. The result is in perfect agreement
with the known answers for the ratios of tensions of D-branes of different
dimensions.
