Euler stratification conjecture for the principal A-determinant

Let $W$ and $W'$ be coefficient points for the varieties $Y_{W,n}$ and $Y_{W',n}$, respectively, and let $E_A$ denote the principal $A$-determinant, whose factors are the discriminantal factors associated to the faces of the relevant polytope. Euler stratification conjecture. If exactly the same factors of $E_A$ vanish on $W$ and $W'$, then

$$\chi(Y_{W,n})=\chi(Y_{W',n}).$$

This conjecture asserts that the Euler characteristic, and hence the ML degree through the signed Euler characteristic formula, is constant on strata determined by the vanishing pattern of the principal $A$-determinant factors. Its resolution status is not specified in the supplied text.