  We propose an algebraic definition of ER=EPR in the $G_N \to 0$ limit, which
associates bulk spacetime connectivity/disconnectivity to the operator
algebraic structure of a quantum gravity system. The new formulation not only
includes information on the amount of entanglement, but also more importantly
the structure of entanglement. We give an independent definition of a quantum
wormhole as part of the proposal. This algebraic version of ER=EPR sheds light
on a recent puzzle regarding spacetime disconnectivity in holographic systems
with ${\cal O}(1/G_{N})$ entanglement. We discuss the emergence of quantum
connectivity in the context of black hole evaporation and further argue that at
the Page time, the black hole-radiation system undergoes a transition involving
the transfer of an emergent type III$_{1}$ subalgebra of high complexity
operators from the black hole to radiation. We argue this is a general
phenomenon that occurs whenever there is an exchange of dominance between two
competing quantum extremal surfaces.
