Kim et al. (2013) [K13] introduced a new methodology for determining peak-brightness absolute magnitudes of type Ia supernovae from multi-band light curves. We examine the relation between their parameterization of light curves and Hubble residuals, based on photometry synthesized from the Nearby Supernova Factory spectrophotometric time series, with global host-galaxy properties. The K13 Hubble residual step with host mass is $0.013pm 0.031$ mag for a supernova subsample with data coverage corresponding to the K13 training; at $ll 1sigma$, the step is not significant and lower than previous measurements. Relaxing the data coverage requirement the Hubble residual step with host mass is $0.045pm 0.026$ mag for the larger sample; a calculation using the modes of the distributions, less sensitive to outliers, yields a step of 0.019 mag. The analysis of this article uses K13 inferred luminosities, as distinguished from previous works that use magnitude corrections as a function of SALT2 color and stretch parameters: Steps at $>2sigma $ significance are found in SALT2 Hubble residuals in samples split by the values of their K13 $x(1)$ and $x(2)$ light-curve parameters. $x(1)$ affects the light-curve width and color around peak (similar to the $Delta m_{15}$ and stretch parameters), and $x(2)$ affects colors, the near-UV light-curve width, and the light-curve decline 20 to 30 days after peak brightness. The novel light-curve analysis, increased parameter set, and magnitude corrections of K13 may be capturing features of SN~Ia diversity arising from progenitor stellar evolution.
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