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Derive, from the resonance structure of a given lattice and the periodic resonance crossing caused by synchrotron motion in a bunched beam, the maximal $\\left|\\Delta Q_{\\mathrm{sc}}\\right|$ compatible with emittance growth below 10 percent and loss below $10^{-3}$ over $N$ turns, and compare with CERN PS and SPS, J-PARC and GSI SIS18 data.","problem_ref":"cff00ad4b461f256f528025a48cf605d41bcdf28b97a318063144f7456c27318","references":"","settled_by":"A scaling law or simulation that matches measured limits in at least three rings with differing lattices and storage times.","status_note":"","title":"Maximum tolerable space-charge tune shift in 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