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The standard model of modern cosmology might be cracked by the recentpersistent hot debate on the Hubble-constant ($H_0$) tension, which manifestsitself as the sound-horizon ($r_s$) tension or absolute-magnitude ($M_B$)tension if deeming the origin of the Hubble tension from modifying the early orlate Universe, respectively. In this Letter, we achieve a fullymodel-independent constraint (fitting a model-independent globalparameterization to a model-independent inverse distant ladder with amodel-independent high-redshift calibration) on late-time models with strongevidence against homogeneous new physics over the $\Lambda$-cold-dark($\Lambda$CDM) model. Further using this model-independent constraint tocalibrate sufficiently local supernovae with corresponding late-time modelsextrapolated below the homogeneity scale, we find surprisingly that, althoughboth $H_0$ tension and $M_B$ tension are absent in our local Universe, acombination of $H_0$ and $M_B$ as the intercept $a_B$ of the magnitude-redshiftrelation exhibits $3\sim 7\sigma$ tension even for the $\Lambda$CDM model. This$a_B$ tension seems to call for local-scale inhomogeneous new physics disguisedas local observational systematics.

No-go guide for the Hubble tension: late-time or local-scale new physics