  The Sun constitutes an excellent laboratory of fundamental physics. With the
advent of helioseismology, we were able to probe its internal layers with
unprecedented precision. However, the current state of solar modelling is still
stained by tedious issues. One of these problems is related to the disagreement
between models computed with recent photospheric abundances and helioseismic
constraints. We use solar evolutionary models as initial conditions for
reintegrations of their structure using Ledoux discriminant inversions. The
resulting models are defined as seismic solar models, satisfying the equations
of hydrostatic equilibrium. They will allow us to better constrain the internal
structure of the Sun and provide complementary information to that of
evolutionary models. These seismic models were computed using various reference
models with different equations of state, abundances and opacity tables. We
check the robustness of our approach by confirming the good agreement of our
seismic models in terms of sound speed, density and entropy proxy inversions as
well as frequency-separation ratios of low-degree pressure modes. Our method
allows us to determine with an excellent accuracy the Ledoux discriminant
profile of the Sun and compute full profiles of this quantity. Our models show
an agreement with seismic data of ~0.1% in sound speed, density and entropy
proxy as well as with the observed frequency-separation ratios. They surpass
all standard and non-standard evolutionary models including ad-hoc changes
aiming at reproducing helioseismic constraints. The obtained seismic Ledoux
discriminant profile as well as the consistent structure obtained from our
procedure paves the way for renewed attempts at constraining the solar
modelling problem and the missing physical processes acting in the solar
interior by breaking free from the hypotheses of evolutionary models.
