Let ${X}^{an}$ be a smooth analytic Calabi-Yau manifold associated with $X_{mer}$. Assuming the equivalence of Gromov-Hausdorff and non-archimedean pictures of collapse presented in Section 5 we have a continuous map $\pi:{X}^{an}\to B$. It gives a $K$-affine structure on $B^{sm}$. The corresponding exact sequence

$$0\to K^{\times}\to Aff_{K}\to(T^{\ast})^{{\bf Z}}\to 0$$

represents a class in $H^{1}(B^{sm},T^{{\bf Z}}\otimes K^{\times})\simeq Ext^{1}((T^{\ast})^{{\bf Z}},K^{\times})$. Pairing with this class gives another homomorphism

$$P^{\prime}:H_{1}(B^{sm},(T^{\ast})^{{\bf Z}})\to K^{\times}=H_{0}(B^{sm},K^{\times})\,\,.$$