Not yet reviewed by Pith; the record is open.

The mass distribution of merging binary black holes is generically predicted to evolve with redshift, reflecting systematic changes in their astrophysical environment, stellar progenitors, and/or dominant formation channels over cosmic time. Whether or not such an effect is observed in gravitational-wave data, however, remains an open question, with some contradictory results present in the literature. In this paper, we study the ensemble of binary black holes within the latest GWTC-3 catalog released by the LIGO-Virgo-KAGRA Collaboration, systematically surveying for possible evolution of their mass distribution with redshift. We specifically focus on two key features present in the binary black hole primary mass distribution -- (1) an excess of $35\,M_\odot$ black holes and (2) a broad power-law continuum ranging from 10 to $\gtrsim 80 M_\odot$ -- and ask if one or both of these features are observed to vary with redshift. We find no evidence that either the Gaussian peak or power-law continuum components of the mass distribution change with redshift. In some cases, we place somewhat stringent bounds on the degree of allowed redshift evolution. Most notably, we find that the mean location of the $35\,M_\odot$ peak and the slope of the power-law continuum are constrained to remain approximately constant below redshift $z\approx 1$. The data remain more agnostic about other forms of redshift dependence, such as evolution in the height of the $35\,M_\odot$ excess or the minimum and maximum black hole masses. In all cases, we conclude that a redshift-dependent mass spectrum remains possible, but that it is not required by current data.