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Determine whether such a law fitted for $N \\le 10^{6}$ predicts $D(N)$ and the resulting intensity decay at $N \\sim 10^{9}$ (about $10^{5}$ s of LHC operation) to within 10 percent, and derive $\\kappa$ from the resonance structure of the map.","problem_ref":"7c76a666c47331c2654443388577edd6af3e7ba9731421380c24cf9ee050572a","references":"","settled_by":"Direct tracking to $10^{9}$ turns of a realistic lattice compared with the extrapolation, plus a derivation of $\\kappa$ from normal-form or resonance analysis.","status_note":"Fitted scaling laws described LHC intensity and luminosity evolution in several fills (2018-2019 papers); a derivation of the exponent and a test at $10^{9}$ turns are missing.","title":"Extrapolating dynamic aperture from a million to a billion 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