This paper extends a recent way of building simple models of a closed “baby” universe in holography to the case of three or more boundary theories. The authors assemble several asymptotically anti‑de Sitter (AdS) “pages” that meet along a common spherical shell, or spine, to prepare a joint quantum state. In a low‑temperature, large‑mass limit the bulk spacetime has a compact central region (the baby universe) surrounded by multiple AdS exteriors; the prepared joint boundary state is called a booklet cosmological state.

To make these states the authors use Euclidean time evolution with a single multilinear operator inserted at the common shell. That insertion and the matching of the pages are governed by a multiway junction condition. For three pages the central region is not a smooth manifold but a branched object, so the construction depends on a choice of how the pages are cut and glued. The physical picture used is a thin spherical dust shell whose largest‑mass saddle produces the closed central region in a semiclassical approximation.

The paper also studies how local excitations in the baby universe are encoded on the several boundary theories. To do that the authors extend an earlier effective‑Gaussian assumption and replace the heavy shell insertion by a single random three‑leg tensor with circular complex Gaussian entries. When restricted to narrow energy windows this model gives states that are Haar distributed on an effective output space and so can be analyzed with random tensor‑network methods.

Using replica‑type entropy calculations and the tensor model, they find concrete quantum information properties. In the simplest three‑arm example, each arm has the same output dimension b and a chosen logical code has dimension K. After a polar normalization the Gaussian map acts like a random isometric encoder, and any two arms typically suffice to recover the logical state with vanishing worst‑case error and high probability when K/b → 0. At fixed finite b, however, exact recovery of a prescribed single‑arm erasure has zero probability. The authors also report that the three‑arm outputs show large pairwise mutual information but typically do not allow perfect extraction of a single Bell pair by local product channels nor an exact GHZ (Greenberger–Horne–Zeilinger) factor by local unitaries.