The unit-coefficient conjecture for the resultant complex

Let ${\mathcal A}_{i}:=\{a\in{\mathbb N}^s:\,\deg(a)=\alpha_i\}$, let $\ell$ be the index of the lattice spanned by $\bigcup_i{\mathcal A}_i$ in $\mathbb{Z}^n$, and let $c\in\mathbb{Q}$ be the constant such that the determinant of the resultant complex is

$$c\cdot {\rm res}_{\alpha_0,\dots,\alpha_n}(F_0,\dots,F_n)^\ell.$$

Unit-coefficient conjecture. The constant $c=\pm1$.

This asserts that the determinant formula for the resultant complex has no nontrivial rational factor, up to sign. The supplied text gives no resolution or further evidence for this assertion.