The fewnomial bound for non-degenerate positive roots

Let $F=(f_1,\ldots,f_n)$ be an $n\times n$ fewnomial system over $\mathbb{R}$ of type $(m_1,\ldots,m_n)$, where each $f_i$ is an $n$-variate $m_i$-nomial in real monomials. A root is non-degenerate when the Jacobian of $F$ at that root has full rank, and the positive orthant is $\mathbb{R}^n_+=\\{x\in\mathbb{R}^n:x_i>0\text{ for all }i\\}$.

Fewnomial root-count conjecture. The maximum number of non-degenerate roots of $F$ in the positive orthant is

$$\prod_{i=1}^n(m_i-1).$$

This is presented as a multivariate generalization of the sharp $m-1$ bound from Descartes' Rule of Signs for a univariate polynomial with $m$ monomial terms. The source gives no resolution status for this bound.