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Small-system numerics often show slower relaxation than simple perturbation theory predicts.","posed_since":"","precise":"Take an integrable lattice Hamiltonian $H_0$ (e.g. the XXZ chain) plus a generic local perturbation g V. Determine the thermalization time $\\tau(g)$ of local observables and the intermediate quasi-stationary state (a deformed generalized Gibbs ensemble) in the limit $L \\to \\infty$ taken before $g \\to 0$, and explain any departure from the Fermi golden rule scaling $\\tau \\sim g^{-2}$. An answer is a controlled kinetic theory that predicts $\\tau(g)$ and the prethermal state for given $H_0$ and $V$, checked against large-scale numerics.","problem_ref":null,"references":"","settled_by":"Large-system numerics (tensor networks or quantum simulation) of $\\tau(g)$ over at least a decade in $g$, matched by a kinetic theory derived from $H_{0}$ and $V$.","status_note":"","title":"How thermalization sets in when integrability is weakly 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