Three-lines property

A rank-3 matroid has the three-lines property if it is simple and every element lies on at least three nontrivial lines (rank-2 flats with at least 3 elements). Non-simple matroids have the value false by convention.

This property matters for the realization-space census. If some element lies on at most two nontrivial lines, deleting it gives a smooth morphism of realization spaces, which is used to transfer positive smoothness results. Three-lines matroids are the terminal cases where no such deletion is available.

Full details: docs/is_three_lines.md.