  Looking at the well-known Hubble tension as a tension in the calibrators of
the cosmic distance ladder, i.e. the absolute magnitude $M$ of standard candles
such as supernovae of Type Ia (SNIa) and the standard ruler represented by the
comoving sound horizon at the baryon-drag epoch, $r_d$, we propose a
model-independent method to measure these distance calibrators independently
from the cosmic microwave background and the first rungs of the direct distance
ladder. To do so, we leverage state-of-the-art data on cosmic chronometers
(CCH), SNIa and baryon acoustic oscillations (BAO) from various galaxy surveys.
Taking advantage of the Gaussian Processes Bayesian technique, we reconstruct
$M(z)$, $\Omega_k(z)$ and $r_d(z)$ at $z\lesssim2$ and check that no
significant statistical evolution is preferred at 68\% C.L. This allows us to
treat them as constants and constrain them assuming the metric description of
gravity, the cosmological principle and the validity of CCH as reliable cosmic
clocks, and SNIa and BAO as optimal standard candles and standard rulers,
respectively, but otherwise in a model-independent way. We obtain:
$\Omega_k=-0.07^{+0.12}_{-0.15}$, $M=(-19.314^{+0.086}_{-0.108})$ mag and
$r_d=(142.3\pm 5.3)$ Mpc. At present, the uncertainties derived are still too
large to arbitrate the tension but this is bound to change in the near future
with the advent of upcoming surveys and data.
