Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'³

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'³ and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'³-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.