# Countable presentation maps and the retained target point

*Transverse measures of foliations*, Theorems 5.35–5.36 and Corollary 5.37, proves the criterion for preserving every source presentation, an explicit standard Borel pullback code, its full image formula and the strict inclusion in the pullback map category. The finite matrix illustrates CP.4–CP.11.

Use Python 3.13.9 and Pillow 12.2.0. Run `python -B draw_countable_probe_maps.py --output-dir out`; `--resources` selects the adjacent labelled-geometric-kernel resources if relocated. The public resources provide the unchanged font, full font notice, CC0 dedication and Python/Pillow notices. Compare PNG/SVG with `../../figures/` and COUNTABLE-PROBE-CHECKS.json with this folder. No private files are read.

All three enumerations, nine codes, class normalization sums and both rational integrals are computed from the displayed finite relation and weights. The normalized full image is 30, whereas raw incidence gives 54. These checks verify the finite example only. The Borel coding, category and full measure arguments are proved in the lesson; the finite model does not parametrize a nonsmooth quotient.