RV data for Kepler-139 (black) from L. M. Weiss et al. (2024). The blue curve is the four-planet model that best fits the RV and TTV data (residual root mean square of 4.4 m s⁻¹). The red curve is the best-fit five-planet model (3.6 m s⁻¹ residual root mean square). The middle panel shows the deviations between the data and the best-fit four-planet model, and the bottom panel shows the same for the five-planet model. The five-planet model provides a significantly better fit to the observed RVs (﹩{\rm{\Delta }}{\chi }_{{\rm{RV}}}^{2}\,=\,77﹩). The gray error bars in the bottom panel show the uncertainties after accounting for the “jitter” term described in Section 4.2.