Testing the uniqueness of the open bosonic string field theory vacuum

The operators K_n are generators of reparameterization symmetries of Witten's cubic open string field theory. One pertinent question is whether they can be utilised to generate deformations of the tachyon vacuum and thereby violate its uniqueness. We use level truncation to show that these transformations on the vacuum are in fact pure gauge transformations to a very high accuracy, thus giving new evidence for the uniqueness of the perturbatively stable vacuum. Equivalently, this result implies the vanishing of some discrete cohomology classes of the BRST operator in the stable vacuum