Before revision:  Under quite general assumptions on the spatial discretization , it is proven that the preconditioned  operator has a condition number of ~O(1),  with only weak dependence on the number of stages or integration accuracy.
After revision:  Under quite general assumptions on the spatial discretization , it is proven that the preconditioned operator has a condition number of ~O(1), independent of the spatial discretization, and with only weak dependence on the number of stages or integration accuracy.