The Supernova Modulus Lever: A Constant Offset, a Fading Shape Signal, and Why the Hubble Tension Is a Calibration Dispute

Type Ia supernovae trace the shape of the expansion history superbly and its absolute scale not at all, unless their intrinsic brightness is calibrated from outside. This paper computes exactly how that division of labour plays out in the current Hubble tension, using the Pantheon+ sample's published scope and the SH0ES absolute-magnitude calibration. Changing the Hubble constant from the Planck value of 67.36 to the SH0ES value of 73.04 km/s/Mpc shifts every predicted distance modulus by the same constant, −0.176 magnitudes, at every redshift from 0.05 to 2.0; equivalently, the Planck history implies a supernova absolute magnitude of −19.429 against the SH0ES calibration of −19.253 ± 0.027, so the entire tension, seen from the supernova side, is a 0.176-magnitude disagreement about one number. The error lever is unforgiving: a magnitude uncertainty maps to a fractional Hubble-constant uncertainty 0.4605 times as large, so a 1 percent Hubble constant needs the absolute magnitude known to 0.0217 mag, and the present 0.027 mag calibration uncertainty alone contributes 1.24 percent. Meanwhile the shape difference between the evolving-dark-energy history favoured in recent joint fits and the standard history peaks at only 0.027 magnitudes near redshift 0.5 and never reaches 0.05 magnitudes anywhere in the Pantheon+ range — smaller than the systematic floor of any current binned Hubble diagram. Supernovae therefore arbitrate the tension only through their calibrators, and this paper quantifies the calibration programme that arbitration requires. The study is computed from stated assumptions and published values; it is not a measurement.