Beyond Toy Models: The Factorization Puzzle and the de Sitter Gap in Black Hole Evaporation

The recent revolution in computing the entanglement entropy of black holes via replica wormholes and the island formula has provided the first semiclassical derivation of the Page curve. Simultaneously, holographic approaches to the de Sitter static patch, such as the doubly scaled SYK model (DSSYK), have proposed finite-dimensional dualities for cosmological horizons. In this paper, we argue that the current enthusiasm for these achievements obscures deep conceptual gaps. We demonstrate that the correspondence between Jackiw-Teitelboim (JT) gravity and Random Matrix Theory (RMT), while structurally consistent, does not constitute a constructive proof of unitarity, and we introduce the factorization puzzle as a reformulation—rather than a resolution—of information loss. Furthermore, we critically evaluate extensions of DSSYK to realistic dS_4, highlighting the absence of a dynamic dictionary for horizon crossing and the lack of consensus on which construction correctly captures bulk gravitational physics. We conclude that while unitarity is now mathematically plausible in reduced-dimensional toy models, the transition to 4D gravity in asymptotically de Sitter spaces remains a non-trivial challenge requiring new holographic architectures.