Universal optimality of the hexagonal lattice A2

Prove that the hexagonal (equi-triangular) lattice A2 is universally optimal, meaning it minimizes energy for all completely monotone interaction potentials of squared distance among lattices in two dimensions.

Background

Universal optimality has been established for E8 and the Leech lattice, enabling exact identification of energy asymptotics constants via Epstein zeta functions in those dimensions. For d=2, analogous results would follow from establishing universal optimality of A2.

The authors highlight that this status for A2 remains conjectural, and confirming it would underpin several asymptotic constants tied to discrepancy and energy in dimension two.