The paper develops a formalism for computing the partition function of three-dimensional quantum gravity with a negative cosmological constant using Virasoro TQFT. The authors compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions, finding a highly non-trivial match. They then apply this formalism to compute the gravity partition functions of various topologies, focusing on multi-boundary wormholes with three-punctured spheres as boundaries. This allows them to quantify the higher moments of the structure constants in the proposed ensemble boundary dual and subject the proposal to thorough checks. Additionally, they investigate the figure eight knot complement as a hyperbolic 3-manifold, showing that the Virasoro TQFT partition function agrees with the partition function computed in Teichmüller theory, providing strong evidence for the equivalence of these TQFTs. They also demonstrate how Dehn surgery on the figure eight knot can produce a large class of manifolds.The paper develops a formalism for computing the partition function of three-dimensional quantum gravity with a negative cosmological constant using Virasoro TQFT. The authors compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions, finding a highly non-trivial match. They then apply this formalism to compute the gravity partition functions of various topologies, focusing on multi-boundary wormholes with three-punctured spheres as boundaries. This allows them to quantify the higher moments of the structure constants in the proposed ensemble boundary dual and subject the proposal to thorough checks. Additionally, they investigate the figure eight knot complement as a hyperbolic 3-manifold, showing that the Virasoro TQFT partition function agrees with the partition function computed in Teichmüller theory, providing strong evidence for the equivalence of these TQFTs. They also demonstrate how Dehn surgery on the figure eight knot can produce a large class of manifolds.