  Using an elementary perturbative open string field theory solution involving
a twistor-like parameter, we study the cohomology of new nilpotent BRST charge
corresponding to the space-time background defined by this solution. The BRST
cohomology of the deformed background automatically cuts off the GSO-odd
spectrum in RNS superstring theory and keeps the GSO-even spectrum intact,
without a need of GSO-projection. The on-shell constraints in the GSO-even
sector get deformed in the new background, corresponding to BRST type
transformations of the low-energy effective action with the ghost-like
commuting spinor parameter satisfying the pure spinor constraint in $d=10$.
