The orbit covariance summability conjecture for Collatz drift increments

Let $\Delta_i$ be the odd-skeleton drift increments along a Collatz orbit, and let $\operatorname{Cov}_{\mathrm{orbit}}(\Delta_0,\Delta_h)$ denote their orbit covariance at lag $h$. Orbit covariance summability conjecture. For every Collatz orbit with odd-step density $\rho<1/\log_2 3$,

$$\sum_{h=1}^{\infty}\left|\operatorname{Cov}_{\mathrm{orbit}}(\Delta_0,\Delta_h)\right|<\infty.$$

The corresponding ensemble covariance estimate is proved in the paper, but the pointwise orbit version is explicitly identified as open and is substantially harder.