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The question is whether the long-lived non-thermal state of FPUT is the equilibrium of the Toda chain, and how fast its conserved quantities drift.","posed_since":"","precise":"Determine whether the pre-thermal state of the $\\alpha$-FPUT chain at small $\\epsilon$ is described by a generalized Gibbs ensemble built from Toda integrals, and find the scaling with $\\epsilon$ and $N$ of the drift time of these integrals, which sets $T_{\\mathrm{eq}}$. An answer is a mechanism with a scaling law consistent with simulations.","problem_ref":null,"references":"","settled_by":"Simulations tracking all Toda integrals in FPUT dynamics, with their drift rates derived from perturbation theory around Toda.","status_note":"Simulations using Toda integrals as slowly varying quantities support this picture (arXiv:2511.08149, 2025); reported scaling exponents differ between studies.","title":"Role of Toda integrals in the FPUT metastable 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