  We study how coarse-graining procedure of an underlying UV-complete quantum
gravity gives rise to a connected geometry. It has been shown, quantum
entanglement plays a key role in the emergence of such a geometric structure,
namely a smooth Einstein-Rosen bridge. In this paper, we explore the
possibility of the emergence of similar geometric structure from classical
correlation, in the AdS/CFT setup. To this end, we consider a setup where we
have two decoupled CFT Hilbert spaces, then choose a random typical state in
one of the Hilbert spaces and the same state in the other. The total state in
the fine-grained picture is of course a tensor product state, but averaging
over the states sharing the same random coefficients creates a geometric
connection for simple probes. Then, the apparent spatial wormhole causes a
factorization puzzle. We argue that there is a spatial analog of
half-wormholes, which resolves the puzzle in the similar way as the spacetime
half-wormholes.
