Simis' normality conjecture for doubly stochastic monomial ideals

Let $S=K[t_1,\ldots,t_s]$ and let $I=(t^{v_1},\ldots,t^{v_s})$ be a monomial ideal whose incidence matrix $A$ is a nonsingular $s\times s$ matrix. Assume the generators have no nontrivial common factor and every variable divides at least one generator. The matrix $A$ is doubly stochastic of degree $d$ when every row sum and column sum equals $d\geq 2$.

Simis' conjecture. If $A$ has entries in $\{0,1\}$ and $\det(A)=\pm d$, then the Rees algebra $S[Iz]$ is normal.

This is presented as a partial converse to the determinant condition known for normal Rees algebras; the text gives a $2$-stochastic supporting result but no resolution of the conjecture.