The uniqueness conjecture for strongly rational holomorphic vertex operator algebras of central charge 24

Let $V$ be a strongly rational, holomorphic vertex operator algebra of central charge $24$, and let $V_1$ denote its weight-one Lie algebra. Uniqueness conjecture. The Lie algebra structure of $V_1$ uniquely determines the vertex operator algebra $V$ up to isomorphism. All 71 affine structures in Schellekens' list are realised, but a complete classification remains open because uniqueness is not known in every case; the paper notes nine open cases, including the Moonshine module $V^\natural$.