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Whether any laboratory material or ordinary lattice model in which each site holds only a few quantum states reaches it is unknown.","posed_since":"2015","precise":"The Maldacena-Shenker-Stanford bound $\\lambda_L \\le 2\\pi k_B T/\\hbar$ holds for regularized thermal OTOCs, and large-N lattice models (SYK chains, Gu, Qi, Stanford 2017) saturate it. For a lattice model with fixed, finite local Hilbert-space dimension (no large-N or semiclassical parameter), determine whether a parametrically wide exponential-growth window exists as $T \\to 0$ and, if so, whether $\\lambda_L \\hbar/(2\\pi k_B T) \\to 1$ can be reached; or prove a bound strictly below 1. Answer: an explicit model or a bound.","problem_ref":null,"references":"","settled_by":"A controlled computation of $\\lambda_{\\mathrm{L}}(T)$ in a microscopic lattice model with finite local dimension, or direct OTOC measurement in a quantum simulator at temperatures where quantum effects dominate.","status_note":"Large-N lattice models saturate the bound; no finite-local-dimension example is known.","title":"Can a lattice with few states per site saturate the chaos 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