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The question is how far below today's best entropy an experiment must go before pairing becomes visible.","posed_since":"","precise":"Let $s_{\\exp}$ be the entropy per site (units of $k_B$) reached in current doped quantum-gas-microscope samples. For the 2D Hubbard model at $U/t = 8$, $\\delta = 0.125$, $t'/t = -0.2$, determine the entropy per site $s*$ below which the d-wave pair correlation length exceeds 10 lattice sites, and hence the required reduction $s_{\\exp} - s*$. Answer: $s*$ with error bars from controlled finite-temperature numerics and the ratio $s_{\\exp}/s*$.","problem_ref":"d688eea65cb382d1f773baba20d2c71c378fc0aa5993687266cf705c35eb87ec","references":"","settled_by":"Controlled finite-temperature numerics (for example diagrammatic Monte Carlo or tensor-network methods with error bars) giving the pair correlation length as a function of entropy per site at the stated parameters.","status_note":"Ground-state DMRG and auxiliary-field quantum Monte Carlo find d-wave order coexisting with partially filled stripes at $t' \\ne 0$ (Xu et al., Science 2024); controlled finite-temperature values of $s*$ are lacking.","title":"Entropy reduction needed to see d-wave correlations in Hubbard 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