Family Donaldson–Smith invariants are independent of the Lefschetz fibration

Let $(X,\omega)$ be a symplectic 4-manifold and let $\alpha\in H^2(X;\mathbb{Z})$. Let $f\colon X'\to S^2$ be a Lefschetz fibration obtained from a sufficiently high-degree Lefschetz pencil on $X$, and let the exceptional divisors of the blowup $X'\to X$ be Poincaré dual to classes $\epsilon_1,\ldots,\epsilon_N$. For $n\geq 0$, write

$$\mathcal{FDS}^{n}_{f}\left(\alpha+\sum_{i=1}^{N}\epsilon_i-2\sum_{k=1}^{n}e_k\right)$$

for the corresponding family Donaldson–Smith invariant. Independence conjecture. These invariants are independent of the choice of $f$ and have a general expression in terms of the Ruan–Tian invariants of $X$. The conjecture would make the family Donaldson–Smith construction an intrinsic nodal analogue of the Gromov invariant, while relating it to Ruan–Tian invariants; the supplied source gives no resolution status.