Moore–Witten type conjecture for generalized Donaldson invariants with massless monopoles

For $N_f=2,3$, let $\pmb{\mathrm{D}}^{N_f}_{m,2n}$ denote the generating function for the generalized $\operatorname{SO}(3)$-Donaldson invariants of $\mathbb{C}\mathrm{P}^2$ with $2N_f$ monopoles, and let $\pmb{\Phi}^{N_f,c,1}_{k,m,2n}$ be the corresponding generating function defined in the source. Moore–Witten type conjecture. The generating function in Equation (generating_function) is the generating function in Equation (generatingfunction2) for the generalized $\operatorname{SO}(3)$-Donaldson invariants of $\mathbb{C}\mathrm{P}^2$ with $2N_f$ monopoles for $N_f=2,3$. The conjecture concerns the expected equality between $u$-plane generating functions and generalized Donaldson invariants; the source later verifies only a weak version for $N_f=2,3$, so the full assertion is not established there.