Nagata-type conjecture for very general quasimonomial valuations

Let $t$ be a real parameter, and let $\widehat\mu(t)$ denote the invariant for a very general quasimonomial valuation introduced in the paper. Nagata-type conjecture for quasimonomial valuations. For all $t\geq 9$,

$$\widehat\mu(t)=\sqrt{t}.$$

The preceding proof shows that this statement follows from the Greuel-Lossen-Shustin conjecture. The supplied text does not establish that conjecture or this consequence unconditionally.