The Repulsion G-B-G conjecture for bad Gram points

Let $g_n$ be a Gram point, and call it bad when it does not satisfy the usual Gram sign condition; call its consecutive neighbours $g_{n-1}$ and $g_{n+1}$ good when they do satisfy it. Define the viscosity of a Gram point by $\mu(g_n)=Z'(g_n)/Z(g_n)$. Repulsion G-B-G conjecture. If $g_n$ is a bad Gram point with good consecutive neighbours $g_{n-1}$ and $g_{n+1}$, then

$$\abs{\mu(g_n)}>4.$$

This is an empirical, non-sharp viscosity bound intended to express a repulsion phenomenon between consecutive zeros of the Hardy Z-function; the source does not provide a proof or resolution.