This paper investigates the Hubble tension, which arises from a discrepancy between the local and global measurements of the Hubble constant $ H_0 $. The authors present a model-independent analysis using a combination of supernova (SNe Ia) and baryon acoustic oscillation (BAO) data, along with cosmic chronometer (CC) calibration, to constrain late-time cosmological models. They find strong evidence against homogeneous new physics beyond the standard ΛCDM model, as the data do not support deviations from ΛCDM in the late Universe. The study also examines the $ a_B $ tension, which is the intercept of the magnitude-redshift relation for SNe Ia. Even though the $ H_0 $ and $ M_B $ tensions are absent in the local Universe, the $ a_B $ tension remains significant, indicating potential local-scale inhomogeneous new physics. The authors argue that this tension could be due to local observational systematics rather than new physics. They further show that the $ a_B $ tension is not explained by the standard ΛCDM model, suggesting that local-scale new physics might be responsible. The analysis uses a model-independent parameterization (PAge model) and a phantom-like dark energy (PDE) model to test the constraints. The results indicate that the PAge model is not significantly better than ΛCDM, while the PDE model is strongly disfavored. The paper concludes that the Hubble tension may not be solely due to new physics in the early or late Universe, but could instead be a result of local-scale inhomogeneous effects. The $ a_B $ tension, which is not resolved by the standard models, suggests that local-scale new physics might be at play. The study emphasizes the importance of further investigations into the local Universe to resolve the Hubble tension.This paper investigates the Hubble tension, which arises from a discrepancy between the local and global measurements of the Hubble constant $ H_0 $. The authors present a model-independent analysis using a combination of supernova (SNe Ia) and baryon acoustic oscillation (BAO) data, along with cosmic chronometer (CC) calibration, to constrain late-time cosmological models. They find strong evidence against homogeneous new physics beyond the standard ΛCDM model, as the data do not support deviations from ΛCDM in the late Universe. The study also examines the $ a_B $ tension, which is the intercept of the magnitude-redshift relation for SNe Ia. Even though the $ H_0 $ and $ M_B $ tensions are absent in the local Universe, the $ a_B $ tension remains significant, indicating potential local-scale inhomogeneous new physics. The authors argue that this tension could be due to local observational systematics rather than new physics. They further show that the $ a_B $ tension is not explained by the standard ΛCDM model, suggesting that local-scale new physics might be responsible. The analysis uses a model-independent parameterization (PAge model) and a phantom-like dark energy (PDE) model to test the constraints. The results indicate that the PAge model is not significantly better than ΛCDM, while the PDE model is strongly disfavored. The paper concludes that the Hubble tension may not be solely due to new physics in the early or late Universe, but could instead be a result of local-scale inhomogeneous effects. The $ a_B $ tension, which is not resolved by the standard models, suggests that local-scale new physics might be at play. The study emphasizes the importance of further investigations into the local Universe to resolve the Hubble tension.