Stopple's type 2 zero curvature estimate for zeros of the zeta derivative

Let $\rho'=\beta'+i\gamma'$ be a sequence of type 2 zeros of $\zeta'(s)$, and let the sum range over the other zeros $\lambda'\ne\rho'$ of $\zeta'(s)$. Stopple's type 2 curvature estimate. If

$$(\beta'-1/2)\log(\gamma')\to 0,$$

then

$$\log(\gamma')\ll \sum_{\lambda'\ne\rho'}\operatorname{Re}\left(\frac{1}{\lambda'-(1/2+i\gamma')}\right).$$

The estimate is identified as sufficient for the forward implication in the paper's reduction of the type 2 zero conjecture to a lower bound on level-curve curvature. It is presented as a conjectural step, and no resolution is supplied.