Ultrastable 2D glasses and packings explained by local centrosymmetry

Using the most recent numerical data by Bolton-Lum \emph{et al.} [Phys. Rev. Lett. 136, 058201 (2026)], we demonstrate that ideal ultrastable glasses in the athermal limit (or ultrastable ideal 2D disk packings) possess a remarkably high degree of local centrosymmetry. In particular, we find that the inversion-symmetry order parameter for local force transmission introduced in Milkus and Zaccone, [Phys. Rev. 93, 094204 (2016)], is as high as $F_{IS}= 0.93546$, to be compared with $F_{IS}=1$ for perfect centrosymmetric crystals free of defects, and with $F_{IS} \sim 0.3-0.5$ for standard random packings. This observation provides a clear, natural explanation for the ultra-high shear modulus of ideal packings and ideal glasses, because the high centrosymmetry prevents non-affine relaxations which decrease the shear modulus. The same mechanism explains the absence of boson peak-like soft vibrational modes. These results also confirm what was found previous work, i.e. that the bond-orientational order parameter is a very poor correlator for the vibrational and mechanical