Sophie, that's similar to the approach I attempted with [#8](https://forum.azimuthproject.org/discussion/comment/18077/#Comment_18077). Does it look right to you? I carry the order on \$$\mathbb{R}^2\$$ back to \$$\mathbb{C}\$$ by a monoid isomorphism, and observe that monoid automorphisms \$$f : \mathbb{C} \to \mathbb{C}\$$ let us produce more partial orders.