  Mathematical inequalities, combined with atomic-physics sum rules, enable one
to derive lower and upper bounds for the Rosseland and/or Planck mean
opacities. The resulting constraints must be satisfied, either for pure
elements or mixtures. The intriguing law of anomalous numbers, also named
Benford's law, is of great interest to detect errors in line-strength
collections required for fine-structure calculations. Testing regularities may
reveal hidden properties, such as the fractal nature of complex atomic spectra.
The aforementioned constraints can also be useful to assess the reliability of
experimental measurements. Finally, we recall that it is important to quantify
the uncertainties due to interpolations in density-temperature opacity (or more
generally atomic-data) tables, and that convergence studies are of course
unavoidable in order to address the issue of completeness in terms of levels,
configurations or superconfigurations, which is a cornerstone of opacity
calculations.
