Smooth over ℤ
Whether the realization-space scheme $X_M \to \operatorname{Spec}\mathbb Z$ is smooth. This means it is flat over $\mathbb Z$ and its fibers over $\mathbb Q$ and over every $\mathbb F_p$ are smooth. The empty space counts as smooth. Loops and parallel elements do not affect the scheme, so a non-simple matroid inherits the value of its simple core.
Smoothness implies absolute regularity, but not conversely. How each value was proved is in rs_smoothness_method. The census is complete for rank 3 on at most 12 elements.
Full details: docs/realization_scheme_singularity_census.md.