  In this proceeding we review and expand on our recent work investigating the
constancy of the absolute magnitude $M_B$ of Type Ia supernovae. In it, we used
baryonic acoustic oscillations (BAO) to calibrate the supernova data and to
check whether the resulting $M_B$ is constant. We used non-parametric methods
like Gaussian processes and artificial neural networks to reconstruct $M_B(z)$.
Here we elaborate on the results by putting them in the context of other
studies investigating possible non-constant $M_B$ and the impact of the
distance-duality relation. We also present some numerical details on the
calculations in the original paper and new non-parametric reconstructions,
including a conservative model-independent fit, confirming its main results.
Notably, we see that $M_B$ remains constant within $1\sigma$, with a possible
jump around $z = 0.01 - 0.15$. Furthermore, the observed distribution of
$M_B(z)$ cannot be described by a single Gaussian, displaying multiple peaks
and tails. The choice of the only remaining parameter -- the sound horizon
$r_d$ leads to a tension in the $M_B-r_d$ plane. Fitting different non-constant
$M_B(z)$ models does not significantly improve the fit and there is no
preference for any of the models by the statistical measures we employ.
