Joyce's piecewise-smoothness conjecture for generic special Lagrangian fibrations

Let $f:M\rightarrow B$ be a generic special Lagrangian fibration of an almost Calabi–Yau $3$-fold, including fibres with singularities, where `generic' has the meaning specified in the paper's Definition 3.4. Joyce's piecewise-smoothness conjecture. Such generic SL fibrations are never smooth, but only piecewise smooth. The claim is motivated by the paper's explicit nonsmooth local models and by a deformation from a smooth fibration to nonsmooth fibrations; the paper offers this as a conjectural description rather than a proved theorem.