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The task is to bound its errors using only independent calibrations.","posed_since":"","precise":"Choose a point $(U/t, \\delta, T/t)$ where unbiased numerical methods lose control (for example $U/t = 8, \\delta = 0.1, T/t < 0.1$). Using Hamiltonian learning of $t, t', U$ and harmonic confinement, entropy thermometry, and stability bounds, give a certified error bar on the nearest-neighbour spin correlator $C(1,0)$ and on the density. 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