Relation to condensed matter approach: CM systems may have analogues to the physics of relative locality.

Both CM versions encode aspect of EFTs in aspects of parameter space topology. Can be related to p-space curvature.

First version: (1) encode low-energy dynamics  in p-space. (2) Stability of low-energy dynamics. (3) Relate topological invariant to p-space curvature.

Second version: (1) encode internal order of condensate in ground state degeneracy (GSD). (2) Demonstrate stability of GSD. (3) Relate GSD to p-space curvature.