Donaldson's hypersymplectic isotopy conjecture

Let $M$ be a compact 4-manifold. A triple $\underline{\omega}=(\omega_1,\omega_2,\omega_3)$ of symplectic forms is a hypersymplectic structure when every nonzero linear combination $a_1\omega_1+a_2\omega_2+a_3\omega_3$, with $(a_1,a_2,a_3)\in\mathbb R^3\setminus\{0\}$, is symplectic. An isotopy is a path of hypersymplectic structures, and cohomologous means that the corresponding components represent fixed cohomology classes.

Donald'son conjecture. For every hypersymplectic structure $\underline{\omega}$ on a compact 4-manifold $M$, there is an isotopy $\underline{\omega}(t)$ of cohomologous hypersymplectic structures for $0\leq t\leq1$, with $\underline{\omega}(0)=\underline{\omega}$, such that $\underline{\omega}(1)$ is hyperkähler. Equivalently, there is a hyperkähler metric on $M$ whose family of Kähler forms is generated by the components of $\underline{\omega}(1)$.

The conjecture says that, up to isotopy and on compact manifolds, hyperkähler triples are essentially the only hypersymplectic structures. The source presents it as a more tractable approach to the preceding folklore conjecture, and does not report a resolution.