Before revision:  We show that in general, the dimension of the affine subspace \mathcal{X}_b containing the solutions x_{b,\omega} can be smaller than \mathbf{Ind}_A(\mathcal{S}) for all b.
After revision:  We show that the dimension of the affine subspace \mathcal{X}_b containing the solutions x_{b,\omega} can be smaller than \mathbf{Ind}_A(\mathcal{S}) for all b.