Extremal lattices as optimal unconstrained sphere packings in dimension 48

A sphere packing in dimension $48$ is a set of congruent non-overlapping balls whose centers form a discrete subset of Euclidean space. An extremal lattice in dimension $48$ is an even unimodular lattice whose minimal norm squared is $2+2\lfloor 48/24\rfloor=6$. Extremal-lattice packing conjecture. Any extremal lattice in dimension $48$ has maximal sphere packing density among all possible sphere packings. This is motivated by the paper's constrained packing theorem and by the absence of any known better configuration; the assertion remains open.