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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 1e-3 over $N$ turns, and compare with CERN PS and SPS, J-PARC and GSI SIS18 data.","problem_ref":null,"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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