Dyadic renormalization conjecture for the perturbed Hofstadter recursion

Let $E(n)$ denote the fluctuation term and let $\epsilon(n)$ denote a bounded perturbation. Dyadic renormalization conjecture. The fluctuation term approximately satisfies

$$E(n)\approx E(n/2)+\epsilon(n).$$

This heuristic relation is intended to explain the observed self-similarity across dyadic scales, but the supplied text gives no resolution.