Host-Mass Dependence of Type Ia Supernova Partition Evolution: Evidence for Environment-Sensitive Cosmological Coupling

This technical note examines whether the coupling between Type Ia supernova light-curve behavior and cosmological expansion depends on host galaxy mass. Using partition and decline-rate observables from a contemporary SN Ia dataset, we test whether supernovae in different host environments exhibit distinct evolutionary behavior.

We find a clear asymmetry: supernovae hosted by high-mass galaxies show statistically significant evolution in the partition parameter (\sim3\sigma), while supernovae in low-mass hosts exhibit no measurable evolution. This host-mass dependence indicates that matter content plays a central role in modulating how supernova light curves couple to expansion history.

At a physically motivated reference epoch (t \sim \tau/3), the observed decline fraction clusters near e^{-1/3} \approx 0.717. This value is treated as a phenomenological reference scale rather than a fitted constant. Its appearance is interpreted as consistent with a volumetric decay process governed by exponential structure, in contrast to surface-level geometric probes.

Heuristic Calculus is introduced as an organizing framework for dimensionless ratios and decay structures, not as a fundamental theory. Selection effects and host-dependent systematics are explicitly discussed, and clear falsifiable predictions are outlined for future large-sample surveys. Independent of interpretation, the results demonstrate that host mass is a critical control variable for understanding supernova cosmological behavior.