Improved parameter range for the eta-expanded identifiability theorem

Let $r$ be the number of coordinates, let $q=(q_i)$ be the vector appearing in Theorem, and let $\eta$ be its expansion parameter. The preceding discussion concerns the separable case, where $H$ is $1$-expanded and $q$ has sum $1$ with $0<q<e$.

Improved eta-expanded theorem. The thesis of Theorem

$$holds if$$

q_i>\frac{1-\eta}{r}

for every $i$. This would improve the sufficient condition $0<q<e/2$ supplied by Theorem

in the separable case and extend the range in which the associated solution is guaranteed to be correct.