Moonshine uniqueness conjecture for the monster vertex operator algebra

A vertex operator algebra is strong-rational if it satisfies the paper's strong rationality conditions, and it is holomorphic if its representation category is trivial. The moonshine module $V^\natural$ is the monster vertex operator algebra. Moonshine uniqueness conjecture. $V^\natural$ is the only strong-rational, holomorphic vertex operator algebra of central charge $c=24$ with no weight-$1$ states. This is a classical uniqueness conjecture and is used as a benchmark for the difficulty of the paper's other conjectures.