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Determine the minimal equilibrium eps_x at $E = 6\\,\\mathrm{GeV}$ and circumference $10^{5}-2 \\times 10^{5}\\,\\mathrm{cm}$ with intrabeam scattering at full current, Touschek lifetime above $1\\,\\mathrm{h}$, and dynamic aperture adequate for on-axis or off-axis injection, and whether eps_x < $10^{-9}$ cm rad (diffraction limit for $\\sim 10\\,\\mathrm{keV}$ photons) is attainable.","problem_ref":"a9bb266f14d9000cb0f87bedef935b4ae9c212c5f10811d7f61372c78d3d3e87","references":"","settled_by":"A lattice optimization with these constraints giving $\\mathrm{eps}_x$ versus circumference, checked against operating fourth-generation rings.","status_note":"","title":"Lowest equilibrium emittance reachable in electron storage 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