Classifying the closure of standard orderings on ${\mathrm{H}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{o}}_{+}(\mathbb{R})$

We characterize a closure of the set of dynamical-lexicographic orderings on ${\mathrm{H}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{o}}_{+}(\mathbb{R})$ and prove the existence of orders outside of it.