Evolution of the lunar semi-major axis over time. The Earth-Moon separation, a_M, is plotted for the three studied models, taking the best-fit values of the free parameters (H, σ_R) as described in Fig. 2 and in the main text. Plotted on top of the evolution curves: Geological inferences of a_M from cyclostratigraphy and tidal laminae data (Tables D.1 and D.2). The shaded envelope corresponds to 2σ-uncertainty in the fitted parameters of the combined model (Appendix C). In the narrow window, we zoom over the most recent 250 Myr of the evolution and make a comparison with the evolution corresponding to explicit numerical tidal modeling using paleogeographic reconstructions (Green et al. 2017) and the prediction of the numerical solution La2004 (Laskar et al. 2004). We note that the integration of a_E extends to 3R_E, but the y-axis is trimmed to start at 15R_E for a better visualization of the geological data.