Constraint to the faint end of the past LF following the method described in Appendix G. Top panels: examples of two radial bins and their associated primordial LFs according to the measured S_N. In each panel, the blue histogram shows the Gaussian LF for the associated value of S_N, with dispersion σ = 0.9 mag and normalised to the luminosity inside the bin. The red histogram shows the skewed LF obtained after dividing the non-normalised Gaussian LF by the GC occupation fraction profile (red dashed line), and then normalising to the bin luminosity. Bottom: Faint-end constraint to the past LF considering the contribution from all annuli (gold), compared to the present-day LF (grey) and the past LF obtained with the simplified method (orange).