Witten's conjecture for many four-manifolds of simple type

We prove that Witten's Conjecture [arXiv:hep-th/9411102] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with $b_1=0$ and odd $b_2^+\geq 3$ follows from our $\mathrm{SO}(3)$-monopole cobordism formula [arXiv:math/0203047] when the four-manifold has $c_1^2\geq \chi_h-3$ or is abundant.