  Entwinement is the entanglement entropy of a subset of gauge-variant degrees
of freedom in a certain twisted state of an orbifold CFT, defined by embedding
the state in a larger Hilbert space with some gauge constraints removed. We
propose an intrinsically gauge-invariant, algebraic definition of entwinement.
Our main piece of evidence is a computation showing that, in a spin system that
resembles the orbifold CFT, the analog of entwinement is the entanglement
entropy of a gauge-invariant subalgebra, which we identify. We review why
entwinement is relevant for the conjecture that entanglement builds spacetime.
