Bentz's zero-free and nonvanishing conjecture for Dirichlet $L$-functions

Let $s=\sigma+it$ be the complex variable for a Dirichlet $L$-function. Bentz's conjecture. The domain

$$\sigma>\frac12,\qquad |t|\leq 1$$

is zero free, and there is no zero at $s=\frac12$ for a Dirichlet $L$-function. The condition concerns zeros near the central line and is introduced as an assumption in work on quadratic residues and the distribution of primes. The source gives no resolution status.