# Reproducing the full-arrow composition diagram

Run `python draw_composition.py` with Matplotlib installed. It writes PNG and SVG to the course figures directory; `--output-dir DIRECTORY` chooses another destination.

Figure 5.25 of **Transverse measures of foliations** types each arrow in the composite cutoff and shows every supported label in the exact m=2, n=3, s=2, t=4 example. The groups are infinite abstract one-unit groupoids; the displayed cutoff supports are finite and complete. Four intermediate cyclic labels contribute to each composite integer. The image factors are 4, 3/4 and 3, and the composite kernel has order 2.

The complete proofs are Theorems 5.30–5.31, equations 5.30.1–5.31.5 and solved Exercises 24–26. Font and software terms are in COMPONENT-TERMS.md and the accompanying full notices.