Posteriors of the mass-radius relation for a subset of the Kepler planetary systems studied in this paper. Black bars show the radii and masses resulting from the analysis of pre-extracted transit timings (Hadden & Lithwick 2017). Green bars show the outcome of RIVERS (RIVERS.deep + the photo-dynamical fit). The priors on masses and eccentricities are set to the default prior and identical in both studies. The blue line shows the earth's composition. The position of Kepler-128 from the top panel is also shown on the bottom panel in purple, with a purple line showing its shift in the mass-radius diagram.