The Geometric Riemann Hypothesis for the fractal zero set

Let $Z_F$ be the fractal zero set constructed from the positive imaginary parts of the non-trivial zeros of $\zeta(s)$ by the recursive four-subinterval construction described in the source. The Riemann Hypothesis is the assertion that all non-trivial zeros of $\zeta(s)$ lie on $\operatorname{Re}(s)=\frac12$. Geometric Riemann Hypothesis. The Riemann Hypothesis is equivalent to the statement that $Z_F$ exhibits statistical self-similarity with specific scaling properties related to the pair correlation of zeros. This is presented as a proposed geometric reformulation, and the source gives no proof of the claimed equivalence.