Maximal valuation conjecture for sufficiently general valuations

Let $\xi$ be a sufficiently general valuation parameter and let $t\ge 8+1/36$. Let $\operatorname{ord}_{\xi,t}$ denote the valuation written in the source, and let maximality mean that it attains the maximal value in the source's valuation-theoretic normalization. Maximal valuation conjecture. The valuation $\operatorname{ord}_{\xi,t}$ is maximal for every such $t$. The source states that this conjecture, proposed in Dumnicki–Harbourne–Küronya–Roé–Szemberg, implies Nagata's conjecture. Its general status is open.