# Actual proper-cutoff graph coordinates

*K-theory of the leaf space*, Section 11AH, proves the actual proper-covariant normalized field, its reduced norm and geometric graph-correspondence completion, then its regular-arrow realization by the cutoff and source-coefficient maps. The connection-preserving outer probability step is proved separately in that section. None of these results asserts a completed physical graph Dirac operator.

Use Python 3.13.9 and Pillow 12.2.0. The unchanged font, complete font notice, full CC0 dedication and Python/Pillow software notices are in the adjacent labelled-geometric-kernel resources. Run `python -B draw_regular_graph.py --output-dir out`; `--resources` may select another copy of those public resources. Compare the PNG/SVG with `../../figures/` and FIGURE-CHECKS.json with this folder. No private inputs are read. The pinned public inputs reproduce all three outputs exactly.

The four rational matrix checks use the stated C2 action, cutoff and fixed arrow/source-coefficient order. They verify V*V=1, LV=VU, the range projection diagonal and the squared cutoff orbit sum. They illustrate the general proofs RG.4–RG.13, rather than deriving a general index from the finite sample. The lower panel records the precise module and coefficient order; the normal connection on the final regularized product, geometric generator and closed graph domain still require proof.