A cosmological intercept tension in local distance ladders

The Hubble tension motivates direct tests of the internal consistency of the local distance ladder. We perform forward and backward consistency checks between Type Ia supernovae in Cepheid host galaxies and the Hubble-flow supernova sample using Pantheon+ data. Within flat $Λ$CDM, we impose Planck-CMB priors on one sample, infer the supernova absolute-magnitude calibration, and propagate it to the other sample to recover the Hubble constant, which should match the input value if the second and third rungs of the distance ladder align perfectly. We examine the impact of host-galaxy peculiar velocities using redshift corrections based on the Manticore-Local reconstruction. These corrections shift the recovered $H_0$ from $74.30^{+1.18}_{-1.20}$ to $71.37^{+1.23}_{-1.18}$ $\mathrm{km\,s^{-1}Mpc^{-1}}$ in the forward analysis and from $60.83^{+0.98}_{-0.97}$ to $63.25^{+0.95}_{-0.93}$ $\mathrm{km\,s^{-1}Mpc^{-1}}$ in the backward analysis, bringing both results closer to the input CMB constraint. Comparing the cosmological intercepts of the magnitude-redshift relation inferred from two rungs of the distance ladder before and after peculiar-velocity corrections, we find that the significance of the discrepancy decreases from $6.8σ$ to $3.9σ$ in the forward check and from $7.3σ$ to $4.3σ$ in the backward check. Peculiar-velocity corrections therefore partially alleviate the intercept tension, while a residual discrepancy persists within the adopted framework. Our results highlight the importance of local velocity modeling and motivate further tests of sample selection and calibration systematics in assessing distance-ladder consistency.