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Whether it can be kept while the plasma pressure is high enough for a reactor and the plasma stays stable is unknown.","posed_since":"","precise":"Quasisymmetry ($\\left|B\\right|$ depending on flux-surface angles only through one fixed linear combination) was achieved in vacuum with symmetry-breaking amplitude about $5 \\times 10^{-5}$ of the field strength (about $0.5\\,\\mathrm{G}$ in a $10^{4}\\,\\mathrm{G}$ field; Landreman and Paul, 2022). Determine whether equilibria exist with quasisymmetry error below $10^{-3}$, volume-averaged $\\beta$ of at least $5\\%$, ideal-MHD ballooning and kink stability, and nested flux surfaces, and map the trade-off frontier between these quantities. An answer is explicit configurations or a demonstrated frontier.","problem_ref":"8f19874020f3124376226da8c9b84816697d2055d998e03fc7094418cf746c1e","references":"","settled_by":"Published equilibria verified by independent equilibrium and stability codes, or a systematic frontier showing incompatibility.","status_note":"Finite-$\\beta$ precisely quasisymmetric equilibria were reported after 2022; simultaneous stability at reactor $\\beta$ is not established.","title":"Precise quasisymmetry together with MHD stability at reactor 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