The High-Z Supernova Search Team used distant Type Ia supernovae to compare the observed relation between luminosity distance and redshift with models of cosmic expansion. Its analysis combined distant events with nearby calibrators and tested how light-curve fitting and sample choices affected the inferred acceleration.[ref]
The physical inference is that sources at a specified redshift were farther away than predicted by relevant nonaccelerating comparison models. Calibration, extinction and population evolution are therefore central to interpreting the brightness difference, rather than secondary corrections to an otherwise direct acceleration measurement.

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  1. Supernova discovery of accelerating expansion
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