Given any function $\tau\in C^{\infty}(\Delta)$ on an edge $\Delta\subset D^{2}\times I$ with $\tau(0)=0$, there is a generic-singular fibration whose base is locally affine isomorphic to the affine manifold with singularities $(\mathbb{R}^{2}\times I,\Delta_{\tau},\mathscr{A})$ of Example 3.9.