  Entwinement was first introduced as the CFT dual to extremal, non-minimal
geodesics of quotiented AdS$_3$ spaces. It was heuristically meant to capture
the entanglement of internal, gauged degrees of freedom, for instance in the
symmetric product orbifold CFT of the D1/D5 brane system. The literature now
contains different, and sometimes inequivalent, field theory definitions of
entwinement. In this paper, we build a discretized lattice model of symmetric
product orbifold CFTs, and explicitly construct a gauge-invariant reduced
density matrix whose von Neumann entropy agrees with the holographic
computation of entwinement. Refining earlier notions, our construction gives
meaning to the entwinement of an interval of given size within a long string of
specific length. We discuss similarities and differences with previous
definitions of entwinement.
