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It is unknown whether they remain special in an infinitely long chain.","posed_since":"","precise":"In the PXP chain, define the fidelity density $f(t) = -\\lim_{L \\to \\infty} (1/L) \\ln \\mid\\langle \\mathrm{Z2}\\mid \\exp(-i H t/\\hbar) \\mid\\mathrm{Z2}\\rangle\\mid^{2}$. Is $f$ at the first revival time strictly smaller than its time-averaged plateau value as $L \\to \\infty$? And does a tower of about $L+1$ eigenstates with entanglement $S = O(\\ln L)$ and Z2 overlap exceeding that of typical eigenstates at the same energy by a factor $\\exp(+a L), a > 0$, persist? Answer yes or no for each.","problem_ref":null,"references":"","settled_by":"An exact construction of the scar tower at all L, or infinite-system tensor-network computation of f(t) showing convergence of the revival dip with bond dimension.","status_note":"","title":"Do PXP scar eigenstates survive as the chain becomes 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