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Whether such systems localize in two dimensions is open.","posed_since":"","precise":"Interacting bosons or fermions on a square lattice in the quasiperiodic potential $V_i = V [\\cos(2 \\pi \\beta x_i + \\phi_x) + \\cos(2 \\pi \\beta y_i + \\phi_y)]$ with irrational $\\beta$: is there $V_c$ such that local memory persists at infinite time as $L \\to \\infty$? Answer yes or no.","problem_ref":"b2c96948618b9bdf65ac085b2effb75c317753d7761e602cdb458f8db86d9bd2","references":"","settled_by":"A size-independent localization crossover over a wide range of L in experiment, together with a theory excluding resonant instabilities in the quasiperiodic case.","status_note":"Agrawal, Vasseur, Gopalakrishnan (PRB 106, 094206, 2022) argue it is stable in $d=2$ at strong modulation, and a 2025 optical-lattice experiment up to $24 \\times 24$ sites saw no clear size drift of the quasiperiodic crossover.","title":"Is quasiperiodic localization stable in two 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