Universal-formula conjecture for lower-level PU(2) monopole pairings

Let $\ell$, $F$, $L_1$, $\mathfrak{s}_0$, $SW(\mathfrak{s}_0\otimes L_1)$, and $Q_X$ denote the level, bundle and line-bundle data, Seiberg–Witten invariant, and intersection form appearing in the Pidstrigach–Tyurin reduction formula. Universal-formula conjecture. The pairing on the right-hand side of that reduction formula is given by a universal formula depending only on $\ell$, $F$, $L_1$, $SW(\mathfrak{s}_0\otimes L_1)$, the intersection form $Q_X$, and invariants of the homotopy type of $X$. Such a formula would provide the universal Seiberg–Witten-theoretic input needed to turn the reduction formula into a relation between Donaldson and Seiberg–Witten invariants; the source presents this as an important step toward proving Witten's conjecture.