Donaldson's hyperkähler deformation conjecture for compact hypersymplectic 4-manifolds

Let $X$ be a compact oriented 4-manifold, and let $\underline{\omega}=(\omega_1,\omega_2,\omega_3)$ be a hypersymplectic structure, meaning a triple of closed 2-forms that spans a maximal positive-definite subspace of $\Lambda^2$ at every point. Suppose

$$\int_X \omega_i\wedge\omega_j=\delta_{ij}.$$

Donaldson's conjecture. There exists a deformation of $\underline{\omega}$ through cohomologous hypersymplectic structures to a hyperkähler triple. This conjecture asserts that, up to isotopy and under the stated normalization, hyperkähler triples are the only hypersymplectic structures on compact 4-manifolds; its general status remains open.