On classification of non-unital amenable simple C*-algebras, III, the range and the reduction

We show that two separable stably projectionless simple C*-algebras A and B with $gTR(A) \le 1$ and $gTR(B) \le 1$ which satisfy the UCT are isomorphic if and only if they have the isomorphic Elliott invariant. A description of Elliott invariant is given. We show all possible simple scaled Elliott invariants can be reached by C*-algebras in the class. We show that these results imply that two separable simple C*-algebras with stable rank one and finite nuclear dimension which satisfy the UCT are isomorphic if and only if they have the same Elliott invariant.