Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha\u27^3

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha\u27^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha\u27^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM