In double-scaled SYK, state-adapted dressed chord operators change the emergent algebra from Type II1 to Type I∞ and restore purity of KM states, unlike generic operators.
Okuyama,Doubled Hilbert space in double-scaled SYK,2401.07403
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Algebraic entanglement entropy from type II1 algebras in double-scaled SYK is matched via triple-scaling limits to Ryu-Takayanagi areas in (A)dS2, reproducing Bekenstein-Hawking and Gibbons-Hawking formulas for specific regions while depending on Krylov complexity of the Hartle-Hawking state.
Establishes a threefold duality linking Krylov complexity growth rate to wormhole velocity and proper momentum in DSSYK holography, with higher moments capturing replica wormholes and Krylov entropy equaling parent-geometry von Neumann entropy after tracing baby universes.