Combinatorial discriminant conjecture for complete-intersection torus fibrations

Let $C^{(i)}_{\lambda_1,\lambda_2,\vec\alpha}$ be a component of the singular locus associated with two divisors in the $i$th part of the nef partition, and let $\pi$ be the torus-fibration projection to $B$. The corresponding components of $\pi(\widehat C^{(i)})$ are open subsets of $(n-1)$-dimensional polytopes meeting two at a time; their deformation lies in an $(n-1)$-dimensional submanifold.

Combinatorial discriminant conjecture. After choosing suitable triangulation data of the dual polytope, the image of each component of $C^{(i)}$ retracts to a codimension-one subset of that submanifold, and the resulting degenerate combinatorial discriminant coincides with the discriminant in the Haase--Zharkov construction.

This gives a combinatorial model for the discriminant of the conjectural torus fibration and relates the geometric degeneration to the Haase--Zharkov construction. The source provides no resolution evidence.