Continuum of transition points for chiral condensates

Construct a natural family of chiral condensates with a continuum of transition points, for example using twisted boundary conditions or a chemical potential, and determine whether it is NIP1 but not NIP2.

Background

The paper proves that the standard family of chiral condensates has a single transition point and is NIP3, whether or not it is stable. It asks whether a continuum of transition points can create the richer topological behavior represented by an NIP1 but non-NIP2 family.

References

Is there a natural family of chiral condensates with a continuum of transition points, obtained for instance from twisted boundary conditions or a chemical potential, that is NIP$_1$ but not NIP$_2$?

— Classification of bipartite observables II: NIP observables and the Todorcevic trichotomy  (2610.12908 - Dueñez et al., 9 Oct 2026) in Section Questions, item 7