# Boundary-controlled joint core

Original proof expression, diagram, generator and exact finite coordinate arithmetic are CC0 1.0, to the extent of rights held. Section11BJ, OJC.1–10 and Exercises285–286 contain the full infinite proofs.

Run python draw_ordinary_joint_core.py --output-dir generated with Python and Pillow. The default resources are ../labelled-geometric-kernel. The PNG uses Python3.13.9 and Pillow12.2. The unchanged shared DejaVu font and embedded SVG font retain the complete font notice; the shared Python and Pillow notices remain. The [CC0 dedication](../labelled-geometric-kernel/LICENSE-CC0.txt) covers original expression; it does not replace technical component terms.

The upper-left path is one unit-coordinate section path with the whole probability-lifted Hilbert vector, rather than separately chosen coordinate paths. The source-essential joint core uses the exact boundary-strip derivative estimate. The genuine groupoid action is transported, and the lower panels show its exact normal-domain obstruction. Ten rational partial sums and four nested support checks illustrate arithmetic only; no finite sample establishes an infinite domain, holonomy comparison or physical Bott pairing.
No externally authored mathematical expression or source PDF is incorporated.