Determine exactness of the first moment-relaxation level

Determine whether the first level of the moment relaxation used for the magic-square clone graphs is exact for the three graphs \(G_{32}\), \(G_{44}\), and \(G_{72}\).

Background

The paper uses a first-level moment relaxation to obtain certified lower bounds on Σ\Sigma for three clone graphs derived from the Mermin–Peres magic square.

The relaxation supplies rigorous bounds, but the authors do not establish whether those bounds equal the true optimized harmonic weights or the exact graph parameters.

References

And is the first level of the moment relaxation already exact for the three graphs of \cref{tab:certified}?

— The Lovász number is not alone: a continuum of Rényi points in the entanglement-assisted spectrum of graphs  (2610.20775 - Mghirbi et al., 14 Oct 2026) in Section 6, paragraph “Small separations”