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In ytterbium and calcium the line is bent, and the cause appears to be nuclear structure, but that has to be predicted quantitatively before the method can find new forces.","posed_since":"2020","precise":"$\\mathrm{Yb}+$ and neutral Yb isotope shifts (Door et al 2025; Kyoto 2026) and $\\mathrm{Ca}+$ isotope shifts (2024) show King-plot nonlinearity at many sigma. Compute the second-order field shift and nuclear-deformation contributions (changes in $r^4$ moments) to the Hz level, so that any residual nonlinearity bounds a Yukawa coupling $y_{e} y_{n}$ of a boson of mass $1\\ \\mathrm{keV}\\ \\text{to}\\ 10\\ \\mathrm{MeV}$.","problem_ref":null,"references":"","settled_by":"Ab initio nuclear and atomic calculations that reproduce the measured nonlinearity patterns across several transitions within the experimental uncertainties.","status_note":"A January 2026 measurement of the Yb $1S0-3P2$ isotope shift excludes a light-boson interpretation of the dominant Yb nonlinearity; the nuclear-structure part is not yet computed to the needed precision.","title":"Nuclear-structure origin of King-plot nonlinearity in Yb and 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