  The dynamics of multiple scalar fields on a flat FLRW spacetime can be
described entirely as a relational system in terms of the matter alone. The
matter dynamics is an autonomous system from which the geometrical dynamics can
be inferred, and this autonomous system remains deterministic at the point
corresponding to the singularity of the cosmology. We show the continuation of
this system corresponds to a parity inversion at the singularity, and that the
singularity itself is a surface on which the space-time manifold becomes
non-orientable.
