## Problem

The Chapter 1 content was inconsistent across sources and contained formatting/notation defects:

- `v0/livre.md` (Chapter 1) contained broken in-text reference formatting (e.g. markdown links like `(...](2)` instead of numeric citations like `(...)[2]`), and a malformed reference pair `...[10](11)`.
- Terminology and typos existed in Chapter 1 (`basins` instead of `bassins`, `Un transformation` instead of `Une transformation`).
- The fixed-point notation was inconsistent (`$C^$` used as a fixed point label).
- The Chapter 1 interpretative section required stricter conditional framing and explicit status of admissibility (the admissible set of transformations is a model parameter), aligned with the corrective chapters 19 and 24.
- `v0/chapitre1.md` and Chapter 1 inside `v0/livre.md` diverged in the interpretative framing and the “paysage” paragraph, causing the same concept to be expressed with different constraints/hypotheses depending on the file.

## Impacts

- Rendered markdown could display incorrect/broken links for citations.
- Readers could misread citation numbers as hyperlinks, and the malformed `[10](11)` could hide the intended paired reference.
- Divergent phrasing across `chapitre1.md` and `livre.md` could reintroduce the “glissement de statut” that the corrective chapters aim to avoid (interpretations read as unconditional claims).
- The missing explicit status of admissibility made it harder to audit what is “data of the model” vs what is “derived”.

## Cause

- Partial/manual edits in `v0/livre.md` changed citation syntax and partially integrated the corrective framing.
- The corresponding source chapter file (`v0/chapitre1.md`) was not updated in lockstep, preserving older wording and older “paysage/cosmogonie” framing.

## Root cause

- No systematic editorial audit enforcing a single citation style and a single vocabulary policy at the chapter boundary.
- No single-source-of-truth enforcement between `v0/chapitre1.md` and the Chapter 1 section embedded in `v0/livre.md`.

## Fix

- Added an explicit “Encadré (statut de l’admissibilité)” in Chapter 1 (book version) to declare admissibility as a model datum and to list minimal structural constraints (invariance, locality, resource bounds, constraint coherence), and to require explicit declaration of any constraint-compatibility procedure when it is introduced.
- Normalized Chapter 1 wording in the book version to keep interpretative passages conditional (hypothesis-indexed), and removed self-positioning language inside the interpretative section.
- Corrected typos/terminology and notation:
  - `Une transformation` (grammar)
  - `bassins` (French terminology)
  - `$C^*$` for fixed point label
  - `cycle limite` (removed stray `*`)
- Normalized in-text citations to bracketed numeric citations and fixed the malformed reference pair formatting.
- Kept `v0/chapitre1.md` as the original source text (by repository policy) and applied the corrections to the compiled book text in `v0/livre.md` only.

## Changed files

- `v0/livre.md`

## Deployment

- Documentation-only change: merge the commit.
- If `v0/livre.md` is regenerated by tooling in the workflow (`v0/compile_livre.py`), the current fix will be overwritten because `v0/chapitre1.md` remains unchanged. To make the fix persistent, the build workflow needs an explicit mechanism (alternate source for Chapter 1, or a deterministic post-processing step during compilation).

## Analysis / verification

- Verify no remaining broken numeric-link citations in Chapter 1:
  - search for patterns like `](2)`, `](20)`, `[10](11)` in `v0/livre.md`
- Verify terminology and typos are fixed:
  - search for `basins`, `Un transformation`, `cycle limite*` in `v0/livre.md`
- Render Chapter 1 markdown and confirm citations appear as numeric bracket references.