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A theory that predicts it reliably in three dimensions is missing.","posed_since":"","precise":"For a linac with laser heater, chicanes and transport, predict the microbunching gain spectrum $G(\\lambda)$ for $\\lambda\\sim 0.1\\text{ to }100\\,\\mathrm{micron}$ including 3D coherent synchrotron radiation, longitudinal space charge, intrabeam scattering and transverse-longitudinal coupling. An answer reproduces measured bunching spectra (for example via coherent optical transition radiation) within a factor of two at each wavelength.","problem_ref":null,"references":"","settled_by":"Start-to-end predictions agreeing with measured gain spectra on at least two XFELs without fitted parameters.","status_note":"1D linear gain theory with laser-heater suppression works for gross trends; quantitative 3D agreement is lacking.","title":"Predictive 3D theory of microbunching gain through 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