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Since localization itself may fail in large systems, the time crystal may only be very long-lived.","posed_since":"2016","precise":"For the disordered periodically driven Ising chain (near-perfect $\\pi$ spin flips plus random Ising couplings, fields and generic perturbations), does the period-doubled response persist for infinite time as $L \\to \\infty$, or is its lifetime finite but parametrically long? Answer yes or no, with the lifetime scaling if no.","problem_ref":"1f9c1e76c74b00ae66cb4c91d5f16800d2158e98f8f6d7588444d3cb03a5ba61","references":"","settled_by":"A determination, by numerics or proof, of the stability of Floquet many-body localization against avalanches in this model.","status_note":"Eigenstate order was observed on a 20-qubit processor (Mi et al., Nature 2022); infinite-time stability depends on the unresolved stability of MBL against avalanches.","title":"Is the many-body-localized time crystal a stable 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