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Whether that argument holds is not settled.","posed_since":"2017","precise":"For interacting lattice models in $d=2$ with independent random on-site disorder (e.g. hard-core bosons with nearest-neighbour hopping and disorder of width $W$), does any finite $W$ give infinite-time localization of local observables as $L\\to \\infty$? The avalanche argument of De Roeck and Huveneers (2017) predicts no. Answer yes or no.","problem_ref":null,"references":"","settled_by":"Experiments or numerics showing whether the apparent localization crossover $W*(L)$ keeps drifting upward with $L$ up to sizes where a thermal region of the predicted critical size is typical.","status_note":"A 2025 optical-lattice study up to 24 x 24 sites reported the random-disorder crossover drifting to higher W with system size, consistent with avalanches (identifier not verified).","title":"Can random disorder localize an interacting system in two 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