Generically stable implies p^{(2)} generically stable?

Determine whether, in arbitrary theories, generic stability of a global type p ∈ S_x(U) implies that its two‑fold Morley product p^{(2)} is also generically stable.

Background

The paper develops stratified ranks localized on generically stable types, assuming that all finite Morley powers p{(n)} are generically stable; this assumption is automatic in NIP but not known in general.

Clarifying whether p{(2)} inherits generic stability from p would remove a technical hypothesis and broaden applicability of the rank machinery beyond NIP.

References

In NIP theories, or even in NTP$_2$ theories (by ), this follows from generic stability of $p$; but it is open in general if generic stability of $p$ implies that $p{(2)}$ is generically stable (a counterexample was suggested in Example 1.7, however it does not work --- see Section 8.1).

— Definable convolution and idempotent Keisler measures III. Generic stability, generic transitivity, and revised Newelski's conjecture (2406.00912 - Chernikov et al., 3 Jun 2024) in Section 2.5 (Generic transitivity and stratified rank localized on p)