Creating this issue at the suggestion of @coreyostrove. CC @pcwysoc.
GST reports define model violation as $N_{\sigma} = (q - k) / \sqrt{2k}$, where $q$ is a $\chi_k^2$-distributed quantity derived from the model under test and the dataset used in model fitting. Normally, $k = n_d - n_p$ is the difference between the number of independent parameters in the dataset and the number of model parameters.
This method for computing model violation doesn't work when $n_d < n_p$, which can happen in early iterations of long-sequence GST with unusual experiment designs. For example, we've seen this with fitting a qutrit model to a qubit experiment design, and when using extremely aggressive fiducial pair reduction in multi-qubit GST. In these situations our reports evaluate $(q - k) / \sqrt{2k}$ at $k=1$, even though $q$ is not necessarily $\chi^2_1$-distributed.
We should figure out how to report model violation in these problematic situations. One option is to just not report model violations for GST depths that have $n_d < n_p$.
Anyone who has thoughts on this subject should feel free to chime in!
