Develops a holographic model demonstrating de Sitter quantum gravity implications.
This paper constructs an exactly solvable holographic model of de Sitter quantum gravity from the {4,3,3} tessellation of S³. Eight cubes tile the three-sphere; placing a perfect tensor at each cell, contracting across shared faces, and designating one cell as the observer produces a holographic model in 3+1 dimensions. Every result is exact: the Ryu-Takayanagi entropy formula holds with zero bulk entanglement, the de Sitter entropy is S = 6 log χ, the Hilbert space dimension is χ⁶ (confirming Banks's finite-dimensionality conjecture as a theorem), the reduced state is maximally mixed (reproducing the Gibbons-Hawking temperature), the Page curve is reproduced exactly, and the observer algebra is the full matrix algebra Mat(χ⁶) with a unique trace state. The proofs use only the perfect tensor property and the graph structure of the tessellation. No approximation, no large-N limit, and no holographic dictionary beyond the tensor network itself is required.
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Alvaro Lozano Rodriguez (2026) studied this question.
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