There exist a compact $K$-analytic surface $X^{an}$, a top degree analytic form $\Omega=\Omega_{X^{an}}$ and a continuous proper Stein map $\pi:X^{an}\to B$ such that the set of $\pi$-smooth points coincides with $Y$ and the induced $K$-affine structure coincides with the one given by $Aff_{K}$.

In other words, the triple $(X^{an},\pi,\Omega)$ is a solution of the Lifting Problem.