  The `cosmic calibration tension' is a $> 5\sigma$ discrepancy between the
cosmological distance ladder built from baryonic acoustic oscillations (BAO)
calibrated by the Planck/$\Lambda$CDM sound horizon ($r_s$) and Type Ia
supernovae (SN1a) calibrated instead with the S$H_0$ES absolute magnitude,
assuming the distance-duality relationship (DDR) holds. In this work, we
emphasize the consequences of this tension beyond the value of the Hubble
constant $H_0$, and the implications for physics beyond $\Lambda$CDM. Of utmost
importance, it implies a larger physical matter density $\omega_m\equiv
\Omega_m h^2$, as both the fractional matter density $\Omega_m$ and $h\equiv
H_0/100$ km/s/Mpc are well constrained from late-time data. New physics in the
pre-recombination era must thus be able to decrease $r_s$ while either reducing
the value of $\Omega_m$, or increasing the value of $\omega_m$. Assuming a
$\Lambda$CDM-like primordial power spectrum, this necessarily results in an
increase in the clustering amplitude $\sigma_8$. Deviations from $\Lambda$CDM
in the late-time expansion history cannot resolve the calibrator tension but
can help relax the required shifts to the matter density and $\sigma_8$: it is
in that sense that a combination of early and late-time new physics may help
alleviate the tension. More precisely, models that modify the pre-recombination
expansion history can accommodate the increase in $\omega_m$ without the need
for additional modifications. It is those models which only affect
recombination that require additional deviations at late-times to be
successful. Hence, the `cosmic calibration tension' points either to a targeted
modification of the pre-recombination expansion history, or to a broader change
affecting multiple cosmic epochs.
