Zariski decomposition conjecture for the class gamma on $\overline{M}_{0,7}^{S_7}$

Let $\overline{M}_{0,7}^{S_7}$ be the symmetric moduli space appearing in the source, and let $S_1,S_2,S_3,D_1,D_2$ be the classes used there. Define

$$\gamma=12S_1+7S_2+2S_3.$$

A Zariski decomposition of $\gamma$ is a decomposition $\gamma=P+N$ into positive and negative parts. Zariski decomposition conjecture for $\gamma$. The decomposition

$$P=\frac{2}{231}(D_1+3D_2)^2,\qquad N=\frac{15}{11}S_2$$

is a Zariski decomposition for $\gamma$. This is proposed as the missing decomposition needed to complete the description of Zariski decompositions in the indicated cone; its status is not resolved in the supplied text.