Bose-Fermi equivalence and interacting string field theory

We show that the bosonic and the fermionic realization of the ghost vertex in the Half-String (HS) Operator approach to Wittenʹs String Field Theory (WSFT) are equivalent. In the process we discover that higher vertices (i.e., N > 3) can be eliminated in WSFT using only the overlap conditions defining the interaction vertex and ghost number counting.