q-Askey deformations of DSSYK produce transfer matrices from basic orthogonal polynomials whose chord numbers map to ER bridge lengths and signal geometric transitions with discrete spectra in sine dilaton gravity.
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Five-loop perturbative computation of DSSYK Krylov complexity equaling wormhole length in sine-dilaton gravity, with cumulants and all-order large-time resummation.
Krylov complexity is equivalent to Lanczos coefficients, return amplitude, and spectral density for operator dynamics, via an explicit recursive algorithm from its t=0 Taylor expansion.
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.
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Probing the Chaos to Integrability Transition in Double-Scaled SYK
A first-order phase transition in the Berkooz-Brukner-Jia-Mamroud interpolating model causes chord number, Krylov complexity, and operator size to switch discontinuously from chaotic (linear/exponential) to quasi-integrable (quadratic) growth.