Schematic representation of the procedure performed in data analysis.

For each country (here we show only local marriages in Spain as a test case) the time series for the fraction of marriages and the fraction of couples are considered, as shown in the left panel. Each dot corresponds to a given province and a given year. We check that, for each province i, Γi,y (or Ω according to the case considered) is monotonic versus time, so to allow the inversion that returns time versus Γ (not shown). Then, time dependence is by-passed by plotting -as raw data- the fraction of marriages versus the fraction of couples as shown in the central panel. Lastly we bin the latter to obtain the coarse grained evolution of the phenomenon, whose data points (yellow circles) have been best fitted against the theory (solid line).