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A<sc>bstract</sc> Recent research has leveraged the tractability of$$ T\overline{T} $$ $T\overline{T}$style deformations to formulate timelike-bounded patches of three-dimensional bulk spacetimes includingdS₃. This proceeds by breaking the problem into two parts: a solvable theory that captures the most entropic energy bands, and a tuning algorithm to treat additional effects and fine structure. We point out that the method extends readily to higher dimensions, and in particular does not require factorization of the fullT²operator (the higher dimensional analogue of$$ T\overline{T} $$ $T\overline{T}$defined in [1]). Focusing ondS₄, we first define a solvable theory at finiteNvia a restrictedT²deformation of theCFT₃onS²×ℝ, in whichTis replaced by the form it would take in symmetric homogeneous states, containing only diagonal energy densityE/Vand pressure (-dE/dV) components. This explicitly defines a finite-N solvable sector ofdS₄/deformed-CFT₃, capturing the radial geometry and count of the entropically dominant energy band, reproducing the Gibbons-Hawking entropy as a state count. To accurately capture local bulk excitations ofdS₄including gravitons, we build a deformation algorithm in direct analogy to the case ofdS₃with bulk matter recently proposed in [2]. This starts with an infinitesimal stint of the solvable deformation as a regulator. The full microscopic theory is built by adding renormalized versions ofT²and other operators at each step, defined by matching to bulk local calculations when they apply, including an uplift fromAdS₄/CFT₃todS₄(as is available in hyperbolic compactifications of M theory). The details of the bulk-local algorithm depend on the choice of boundary conditions; we summarize the status of these in GR and beyond, illustrating our method for the case of the cylindrical Dirichlet condition which can be UV completed by our finite quantum theory. 

A bstract We obtain microstates accounting for the Gibbons-Hawking entropy in dS 3 , along with a subleading logarithmic correction, from the solvable T $$ \overline{T} $$ T ¯ + Λ 2 deformation of a seed CFT with sparse light spectrum. The microstates arise as the dressed CFT states near dimension ∆ = c/ 6, associated with the Hawking-Page transition; they dominate the real spectrum of the deformed theory. We exhibit an analogue of the Hawking-Page transition in de Sitter. Appropriate generalizations of the T $$ \overline{T} $$ T ¯ + Λ 2 deformation are required to treat model-dependent local bulk physics (subleading at large central charge) and higher dimensions. These results add considerably to the already strong motivation for the continued pursuit of such generalizations along with a more complete characterization of T $$ \overline{T} $$ T ¯ type theories, building from existing results in these directions.