Solution (source code)

= Solution

The three stable fields are:
$$
\boxed{\begin{aligned}
\text{nepheline: }&x<-5.515,\quad y>3.44-x,\\
\text{albite: }&x>-5.515,\quad y>-7.59-3x,\\
\text{corundum: }&y<\min(3.44-x,-7.59-3x).
\end{aligned}}
$$
Equalities give the stable coexistence boundaries described above. In particular, a point between the two descending line extensions is not automatically a fourth field: only the lower line borders the stable <corundum> region on each side of the intersection. The free-energy comparisons, rather than the appearance of the complete straight-line sketch, select the stable <mineral>.