  DA-type white dwarfs account for 80% of all white dwarfs and represent, for
most of them, the ultimate outcome of the typical evolution of
low-to-intermediate mass stars. Their internal chemical stratification is
strongly marked by passed, often uncertain, stellar evolution processes that
occurred during the helium (core and shell) burning phases, i.e., from the
horizontal branch through AGB and post-AGB stages. Pulsating white dwarfs, in
particular the "cool" DA-type ZZ Ceti variables, offer an outstanding
opportunity to dig into these stars by fully exploiting their asteroseismic
potential. With our most recent tools dedicated to that purpose, we show that a
complete cartography of the stratification of the main constituents of a white
dwarf can be inferred, leading in particular to strong constraints on the C/O
core structure produced by the processes mentioned above. This opens up the way
toward a systematic exploration of white-dwarf internal properties.
