Airy density from a 3D gravity sum over geometries

Establish whether the sum over three-dimensional geometries in the universal Schwarzian sector of three-dimensional gravity reproduces the Airy density of states at the spectral edge.

Background

The paper suggests exploring higher-dimensional analogs of the JT gravity phenomena. In particular, the universal Schwarzian sector of 3D gravity has been proposed as a promising arena where similar nonperturbative spectral physics may appear.

The authors cite a conjecture that an analogous sum over 3D geometries reproduces the Airy edge density of states, indicating an open direction to rigorously establish this correspondence.