Determining the fate of the Pauling entropy in the classical spin ice material Dy 2 Ti 2 O 7 with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T ≈ 0.15 K, but recent experiments by Pomaranski et al. suggest an entropy recovery over long timescales at temperatures as high as 0.5 K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35 K=10 6 s and 0.5 K=10 5 s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez et al. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions. DOI: 10.1103/PhysRevLett.121.067202 The properties of ice-rule states, such as water ice [1,2] and spin ice [3][4][5], provide a strong contrast with the conventional paradigm of condensed matter. Instead of broken symmetry, entropy that vanishes in accord with the third law, exponentially decaying correlations, and wavelike excitations, one finds Coulomb phase correlations [6], finite entropy [1,5], and pointlike fractional excitations (monopoles) [7,8]. The mapping between the hydrogen bonding network and spin configurations [4,9] and the resultant identical residual (Pauling) entropy [5] are cornerstones of spin ice physics, posing fundamental questions including how a realistic Hamiltonian can lead to practical evasion of the third law, and whether the entropic state is metastable. Because the low-temperature dynamics of spin ice depends on a vanishing number of thermally excited monopoles, relaxation becomes slow at low temperatures [2,10], and sensitivity to sample variations is enhanced [11,12]; both effects may mask the true equilibrium state. While the third law ground state of water ice can be accessed by doping that increases dynamics [9], the fate of the residual entropy in the spin ice Dy 2 Ti 2 O 7 [5] is unknown. Because of these experimental challenges, the problem of third law ordering in ice-type systems may best be addressed by a careful collaboration of experiment and theory, designed to accurately model the system and extrapolate properties beyond the experimental range.The spin ice state of Dy 2 Ti 2 O 7 [3-5] is a consequence of frustration arising from the competition between the Isinglike crystal field anisotropy [13,14], exchange, and dipolar interactions [15,16]. These ingredients can be described by a clas...