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Long-range dipolar forces predict an ordered state below about 0.2 K, but experiments struggle to reach equilibrium there.","posed_since":"2001","precise":"In $\\mathrm{Dy_2Ti_2O_7}$, determine whether thermal equilibrium below 0.5 K approaches the ordered state predicted by the dipolar spin-ice model (transition near 0.18 K) with loss of the Pauling entropy $(R/2)\\ln(3/2)$ per mole Dy, or retains a disordered ice manifold. An answer is the equilibrium entropy and any ordering wavevector as $T \\to 0$.","problem_ref":"31a3a46024546948749390b73fc545a6b30dc5d0bfdeb81438cb4ac0924ce169","references":"","settled_by":"Equilibrium heat capacity and neutron scattering below 0.3 K after controlled long annealing, compared with Monte Carlo of the fitted dipolar model.","status_note":"Pomaranski et al. (Nature Physics 2013) found the residual entropy is lost after long equilibration without detecting the predicted order.","title":"Does classical spin ice $\\mathrm{Dy_2Ti_2O_7}$ order or keep its Pauling 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