Likelihood-Robust Isolation of the Host-Galaxy Mass Step in Type Ia Supernovae

I present a likelihood-robust isolation of the host-galaxy mass step in Type Ia supernovae using the Pantheon+ / SH0ES compilation. Rather than invoking discrete supernova sub-populations, modified gravity, or dust-driven attenuation, I model the full population with a heavy-tailed Student-t likelihood that explicitly includes intrinsic scatter and an environment-dependent zero-point offset. I perform a systematic sweep over the Student-t degrees of freedom ν, spanning strongly heavy-tailed to Gaussian limits, and evaluate the host-mass step under both raw and post-corrected magnitude constructions. In the raw-magnitude analysis, I detect a stable, nonzero mass step of ∆M ≃ −0.08 mag across all ν, with permutation p-values ≃ 5 × 10−4 and no sensitivity to tail-heaviness or intrinsic-scatter treatment. In contrast, when using post-corrected magnitudes that already include a mass-step correction, the inferred offset is consistent with zero for all ν. These results decisively rule out discrete “twin” populations, likelihood mis-specification, unmodeled intrinsic scatter, and residual environmental structure as explanations for the mass step, demonstrating that Type Ia supernovae are consistent with a single heavy-tailed population whose absolute magnitude exhibits an environment-dependent zero-point offset in high-mass host galaxies.