Expected dimension over ℤ

An incidence count predicting the dimension of the rank-3 realization scheme over $\operatorname{Spec}\mathbb Z$, based on Ford's expected codimension of matroid varieties. For a connected simple rank-3 matroid on $n$ elements it is $2n - 7 - \sum_H (|H|-2)$, where $H$ runs over the rank-2 flats. Over a fixed field the count is one less; the extra dimension is the arithmetic direction. Non-simple matroids are simplified first, and disconnected cases are handled separately.

This is not an actual dimension. Incidence theorems (e.g. Pappus) can make the true dimension larger, and negative values are meaningful. Compare rs_dim.

Full details: scripts/expected_dimension.jl, docs/characteristic_dimensions.md.