Abstract
We present a new formalism, alternative to the old thermodynamic-Bethe-ansatz-like approach, for solution of the spectral problem of planar $\mathcal{N}=4$ super Yang-Mills theory. It takes a concise form of a nonlinear matrix Riemann-Hilbert problem in terms of a few $Q$ functions. We demonstrate the formalism for two types of observables\char22{}local operators at weak coupling and cusped Wilson lines in a near Bogomol'nyi-Prasad-Sommerfield limit.

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