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Excluding Hypothetical Light Boson Interpretation of Yb King Plot Nonlinearity with the ${}^1S_0 \leftrightarrow {}^3P_2$ Isotope Shift Measurement

We present precision spectroscopy and isotope shift measurement of the ${}^1S_0 \leftrightarrow {}^3P_2$ clock transition in neutral ytterbium ($\mathrm{Yb}$) atoms. By revealing a magic wavelength at $905.4(2)$ nm, we successfully achieve the atomic spectrum narrower than $100$ Hz. The interleaved clock operation between isotopes allows us to determine isotope shifts of four bosonic isotope pairs at Hz-level uncertainties, which is combined with those of other four ultra-narrow transitions in $\mathrm{Yb}$ and $\mathrm{Yb}^+$ to construct the King plot. Importantly, the new isotope shift data reported in this work is a key to exclude the possibility of attributing the observed nonlinearity of the three-dimensional King plot solely to the new physics, while the previous works rely on the other terrestrial bound set by the neutron scattering and $(g-2)_e$ measurements. This work paves the way for the effective use of precision isotope shift data in the King plot analysis and stimulates further measurements in $\mathrm{Yb}$ and other elements.