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Is SMAR ∩ coSMAR equal to Γ2?

Determine whether the intersection of support-margin classes SMAR and coSMAR coincides exactly with the class Γ2 of problems with constant γ2-norm; i.e., prove or refute SMAR ∩ coSMAR = Γ2.

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Background

The authors introduce SMAR and coSMAR as “one-sided” margin analogues and show Γ2 ⊆ SMAR ∩ coSMAR. Whether this containment is tight is unclear and would clarify the geometric characterization of Γ2 via support-margin representations.

A positive resolution would unify two perspectives on constant-margin-like behavior; a negative one would separate γ2 from support-margin frameworks.

References

This suggests some new open problems. Another question suggested by new classes in \cref{fig:hierarchy} is whether $\SMAR \cap \coSMAR = \Gamma_2$.

— Sign-Rank of $k$-Hamming Distance is Constant (2506.12022 - Göös et al., 1 May 2025) in Section 6.4 (Open Problems)