The converse subsequence quantile conjecture for point-stationary circle packings

Let $[\boldsymbol{G},\boldsymbol{o}]$ be a rooted random graph with a point-stationary circle packing (CP), and let its CP-cocycle be $\boldsymbol{c}$. The notation $\boldsymbol{c}$ denotes the cocycle associated with the point-stationary CP, and

is the quantile condition introduced earlier in the paper. **Converse quantile conjecture.** If $[\boldsymbol{G},\boldsymbol{o}]$ has a point-stationary CP whose CP-cocycle is $\boldsymbol{c}$, then the quantile condition

holds along some subsequence.

This is stated as a converse to the paper's tightness theorem. The supplied text does not indicate whether the claim has been proved or remains open.