# Projective exhaustion and the tube-injection prerequisite

Open `index.html` through a local HTTP server. The main reading is `projective-exhaustion-and-the-finite-chain-tube-receiver.html`, with its editable Markdown source beside it. Supporting readers are under `providers/`, and their sources are under `sources/`. The packet includes the selected complete duality and tubular-neighbourhood sections identified in those readers' notices.

This partial prerequisite gives elementary arguments, the stated normal Thom and tubular-neighbourhood construction, worked examples and solutions. The tube-injection deduction assumes the declared ordinary Morse handle input H. It does not establish H, general rational-form spanning, the affine/projective C8 comparison or component constancy. Each supporting reading states its authorship and component terms.

Figure 1 is a radial section of the projective exhaustion. Figure 2 shows the phase-square parameterization of the product tube and its dimension ledger. Their coordinates and constants are specified in the captions and `figures/geometry.json`. Editable figure sources are in `make_figures.py`; Python, NumPy and Matplotlib produce the PNG/SVG pairs. Run `python make_figures.py --out fresh-figures` to reproduce them. The readers retain selectable mathematical text and horizontally scrollable formulas; SVGs support magnification.

## Plurisubharmonic reading

The current reading is `providers/plurisubharmonic-functions-and-stein-manifolds-shell-corrected.html`, with editable source at `sources/plurisubharmonic-functions-and-stein-manifolds-shell-corrected.md`. It includes the continuous-exhaustion lower-bound argument, the exact relative shell calculation and the complex-disc maximum principle used by the punctured-plane exercise. The separately marked historical source and reader remain available at the corresponding filenames without `-shell-corrected`.

Programme prose, diagrams and the figure renderer are CC0-1.0. Source-author credits and component terms remain with the readings. MathJax and figure-font licences are supplied separately.