The singular fibres over $\mathfrak{D}\setminus\{0\}$ have non-isolated singularities by $T^{2}$-invariance. This does not contradict Joyce’s critique, since the Ooguri-Vafa type metric on the positive vertex is not a generic metric (cf. review Section 1.1.5). But when we glue the Ooguri-Vafa type metric into the global Calabi-Yau metric on a degenerating 3-fold (cf. review Section 1.1.6), the exponentially small corrections to the complex structure will destroy $T^{2}$-invariance. We then expect the singularity structure of the SYZ fibration to be drastically changed, and in particular its discriminant locus thickens into a ribbon around $\mathfrak{D}$ as predicted by Joyce [14].