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Whether some three-dimensional system can do it was open for over twenty years.","posed_since":"","precise":"Does there exist a family of geometrically local Hamiltonians on qubits in $R^{3}$, with bounded interaction strength and qubit density, whose ground space encodes at least one qubit with a memory time, under a weakly coupled thermal bath (Davies dynamics), that grows as $\\exp(c L^{b})$, $b > 0$, at some fixed temperature $T > 0$?","problem_ref":"83eee09d9c1695b9e7ca17cc4adae820fb0e56631d118528edcbb4eb3c9a4cc7","references":"","settled_by":"A proof of exponential memory time for an explicit 3D local Hamiltonian, checked independently.","status_note":"A May 2026 preprint (Balasubramanian, Davydova and Lin, arXiv:2605.10943) constructs a non-translation-invariant 3D Pauli stabilizer Hamiltonian with provably exponential memory time below a critical temperature; independent verification is pending.","title":"Existence of a self-correcting quantum memory in three 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