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A peculiar transition seen in simulations in 1992 suggested this, but whether a true glass phase exists is unknown.","posed_since":"1992","precise":"For dtheta_i/dt = $\\omega_i$ + sum_j $J_{ij}$ sin(theta_j - theta_i) with Gaussian omega_i of unit variance and symmetric Gaussian couplings J_ij of variance $J^2/N$ (the Daido model), determine whether for $J$ above some $J_g$ the $N \\to \\infty$ dynamics has a frozen component, for example a nonzero limit of $C(\\tau) = (1/2N) \\operatorname{sum}_i \\langle \\cos(\\theta_i(t+\\tau) - \\theta_i(t))\\rangle$ as $\\tau \\to \\infty$. The volcano transition near $J = 1.3$ (a change in shape of the local-field distribution) is established; its relation to a glass phase is the question. Answer: yes or no, with $J_g$.","problem_ref":null,"references":"","settled_by":"A dynamical mean-field (cavity) solution at large J showing presence or absence of a persistent correlation plateau, confirmed by large-N simulations.","status_note":"A 2024 dynamical-cavity analysis explained the volcano transition and found no persistent correlation in the accessible range, arguing it does not imply a glass (arXiv:2310.09079).","title":"Existence of an oscillator glass in randomly coupled phase 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