  We show that the CPE class $\alpha$ of Barbieri and Garc\'ia-Ramos contains a
one-dimensional subshift for all countable ordinals $\alpha$, i.e.\ the process
of alternating topological and transitive closure on the entropy pairs relation
of a subshift can end on an arbitrary ordinal. This is the composition of three
constructions: We first realize every ordinal as the length of an abstract
"close-up" process on a countable compact space. Next, we realize any abstract
process on a compact zero-dimensional metrizable space as the process started
from a shift-invariant relation on a subshift, the crucial construction being
the implementation of every compact metrizable zero-dimensional space as an
open invariant quotient of a subshift. Finally we realize any shift-invariant
relation $E$ on a subshift $X$ as the entropy pair relation of a supershift $Y
\supset X$, and under strong technical assumptions we can make the CPE process
on $Y$ end on the same ordinal as the close-up process of~$E$.
