Gö​ttsche's generating-function conjecture for the Kotschick–Morgan wall-crossing term

Let $X$ be a $4$-manifold with $b_+(X)=1$ and $b_1(X)=0$, let $\xi\in H^2(X,\mathbb Z)$ satisfy $\xi^2<0$, and let $\lambda_{[X]}(q)$ be the power-series factor associated with the equivalence class $[X]$. Let $n_2$ be the number of $2$-torsion points in $H^2(X,\mathbb Z)$. Gö​ttsche's conjecture.

$$\lambda_{[X]}(q)=n_2\frac{f(\tau)\Delta(2\tau)^2}{\Delta(\tau)\Delta(4\tau)}.$$

Here $q$ and $\tau$ are related by the modular-form convention used in the paper, and $f$ and $\Delta$ are the modular forms defined there. The conjecture proposes a simple dependence of $\lambda_{[X]}$ on the torsion of $H^2(X,\mathbb Z)$; the supplied text gives no resolution status.