The irreducibility conjecture for toric subresultants

Let ${\mathbb A}$ be the coefficient ring, let $P_h\in{\mathbb A}$ denote the factor associated with a monomial $h$ of critical degree, and let $\ell$ be the index of the lattice spanned by the supports in the ambient lattice. Irreducibility conjecture. If $P_h$ is not identically zero, then it is an irreducible element of ${\mathbb A}$. In particular, when $\ell=1$, every subresultant ${\mathcal S}_h$ is irreducible.

The assertion concerns the factorization of nonzero toric subresultants in the coefficient ring. The supplied text gives no resolution or status evidence beyond the stated conjectural formulation.