The uniqueness conjecture for the densest lattice covering in dimension 6

Let $Q^{c1}_6$ be the positive quadratic form defining the lattice covering studied in the paper, and let lattice coverings in dimension $6$ be compared by their covering density. Uniqueness conjecture. The PQF $Q^{c1}_6$ provides the unique least dense lattice covering in dimension $6$. The preceding theorem gives an upper bound of $2.464801$ for its covering density, while the conjecture, motivated by computational experiments and the structural results discussed in the paper, asserts both optimality and uniqueness.