Simis' Cremona-map criterion for normal Rees algebras

Let $S=K[t_1,\ldots,t_s]$, let $I=(t^{v_1},\ldots,t^{v_s})$, and let $F=(t^{v_1},\ldots,t^{v_s})$ define the associated rational monomial map

$$F\colon \mathbb{P}^{s-1}\dasharrow\mathbb{P}^{s-1}.$$

A Cremona map is a rational map admitting an inverse rational map with source $\mathbb{P}^{s-1}$.

Simis' reformulation. The map $F$ is a Cremona map if and only if the Rees algebra $S[Iz]$ is normal.

This is explicitly given as a reformulation of Simis' doubly stochastic conjecture; the supplied text provides supporting results but no resolution.