Regular realization scheme

Whether the realization-space scheme $X_M$ is regular as an absolute scheme, i.e. every local ring is regular. Smooth over ℤ implies regular, but not conversely: $\mathbb Z[x,y]/(xy-p)$ is regular although its fiber at $p$ is singular. So a singular fiber does not by itself prove non-regularity. That requires a separate mixed-characteristic Jacobian test. The empty scheme counts as regular.

Complete for rank 3 on at most 11 elements, except 208 unresolved records (NULL). Not the matroid property regular. See rs_regularity_method.

Full details: docs/realization_scheme_singularity_census.md.