Conjecture on codimension-one affine singularities

Assume that the singular set of the limiting space has a stratification $B^{sing}=B^{sing}_{n-1}\cup B^{sing}_{\le n-2}$, where $B^{sing}_{n-1}$ consists of the $(n-1)$-dimensional strata. Conjecture on codimension-one affine singularities. Near each point of $B^{sing}_{n-1}$, the ${\bf Z}$-affine structure is modeled on a finite book $\bigcup_{i\in I}{\bf R}^{n-1}\times{\bf R}_{\ge0}$ with common spine ${\bf R}^{n-1}\times\{0\}$, and the affine structure on the smooth part $\bigsqcup_{i\in I}{\bf R}^{n-1}\times{\bf R}_{>0}$ is the natural one. This is a proposed local model for codimension-one singularities of the affine structure; it is presented among the authors’ desired properties rather than as an established theorem.