arXiv:2611.13068v1 Announce Type: new Abstract: We solve the ten martini problem for the positive-Lyapunov part of the spectrum of any nonconstant real analytic one-frequency Schr\"odinger operator. The proof uses the intrinsic symplectic structure of the dual center of Ge--Jitomirskaya [28] and extends the Kotani--almost-reducibility strategy of Ge--Jitomirskaya--You [30] from two-dimensional centers to arbitrary finite center dimension.
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