Formal duality of densest sphere packings

Determine whether the stealthiest particle configuration is always a formal dual of the densest sphere packing.

Background

The paper constructs a 20-dimensional periodic configuration that is formally dual to Vardy's sphere packing and is consequently stealthier than any known 20-dimensional lattice at equal particle density. This raises the possibility of a general relationship between densest sphere packings and stealthiest configurations. The authors note that such a principle appears unlikely because densest sphere packings need not possess formal duals, but they do not resolve the possibility.

References

We cannot rule out the possibility that the stealthiest configuration is always a formal dual of the densest sphere packing, but that seems exceedingly unlikely.

— The stealthiest particle configurations in 8 and 24 dimensions  (2609.03121 - Cohen et al., 2 Sep 2026) in Section 1, Introduction