  We present SALT2X, an extension of the SALT2 model for SN Ia supernova light
curves. SALT2X separates the light-curve-shape parameter x1 into an x1r and x1f
for the rise and fall portions of the light curve. Using the Joint Lightcurve
Analysis (JLA) SN sample, we assess the importance of the rising and falling
portions of the light curve for cosmological standardization using a modified
version of the Unified Nonlinear Inference for Type Ia cosmologY (UNITY)
framework. We find strong evidence that x1r has a stronger correlation with
peak magnitude than x1f. We see evidence that standardizing on the rise affects
the color standardization relation, and reduces the size of the host-galaxy
standardization and the unexplained ("intrinsic") luminosity dispersion. Since
SNe Ia generally rise more quickly than they decline, a faster observing
cadence in future surveys will be necessary to maximize the gain from this
work, and to continue to explore the impacts of decoupling the rising and
falling portions of SN Ia light curves.
