  We construct a background for M-theory that is moduli free. This background
is then shown to be related to a topological phase of the $\mathrm{E}_{8(8)}$
exceptional field theory (ExFT). The key ingredient in the construction is the
embedding of non-Riemannian geometry in ExFT. This allows one to describe
non-relativistic geometries, such as Newton-Cartan or Gomis-Ooguri-type limits,
using the ExFT framework originally developed to describe maximal supergravity.
This generalises previous work by Morand and Park in the context of double
field theory.
