LAUSR

We present the vacuum of a two-dimensional conformal field theory as a network of Wilson lines in $SL(2,\mathbb{R})\ifmmode\times\else\texttimes\fi{}SL(2,\mathbb{R})$ Chern-Simons theory, which is conventionally used to study gravity in three-dimensional anti--de Sitter space. The position and shape of the network encode the cutoff scale at which the ground state density operator is defined. In the framework of query complexity, a general argument relates the ``density of complexity'' of the network to the extrinsic curvature of the cutoff surface in ${\mathrm{AdS}}_{3}$, which accords with the holographic $\mathrm{complexity}=\text{volume proposal}$.