  What if it were possible to remove and replace the topological underpinnings
of our spacetime theories just as easily as one can switch between different
coordinate systems? Grimmer (2023) claims this is possible by using his
recently introduced ISE Methodology. Moreover, he claims that these novel
topological redescription techniques can be used to provide new support for a
roughly Kantian view of space and time; Rather than corresponding to some
fundamental substances or relations in the world, we can see the spacetime
manifolds which routinely appear in our best scientific theories as merely
being an aspect of how we represent the world. This view of spacetime topology
is intended to parallel a roughly Humean view of laws and a broadly
dynamics-first view of geometry; The spacetime manifolds which feature in our
best theories reflect nothing metaphysically substantial in the world beyond
them it being one particularly nice way (among others) of codifying the
dynamical behavior of matter.
  This paper will assess the technical side of this program. I will first
identify the range of spacetime theories which can be output by the ISE
Methodology. These include every spacetime theory which meets a very weak
spacetime-kinematic compatibility condition. Next, I will prove that
ISE-relatedness is an equivalence relation over this range and give an exact
characterization of its equivalence classes. As I will prove, two spacetime
theories are ISE-equivalent if and only if 1) they both have
spacetime-kinematic compatibility, and 2) there is a certain kind of
dynamics-preserving isomorphism between their kinematic structures. Hence, the
ISE Methodology allows us to access effectively every possible spacetime
framing of a given theory's kinematical and dynamical content, bounded only by
a weak spacetime-kinematic compatibility condition.
