EKR robustness of alternating groups

Determine whether Alt(n) is EKR robust for all sufficiently large n.

Background

The paper raises the analogous robustness problem for alternating groups after discussing the unresolved behavior of large symmetric groups. No general result establishing or refuting robustness for sufficiently large alternating groups is provided.

References

Question 7.5. For n sufficiently large, is Alt(n) EKR robust?

— A new measure of robustness of Erdős--Ko--Rado Theorems on permutation groups  (2502.14582 - Gunderson et al., 20 Feb 2025) in Question 7.5, Section 7