# Document Improvement — Reference Checklist

Condensed rules for correcting scientific and technical documents. Source: project writing guide.

## Titles

| Incorrect | Correct |
|-----------|---------|
| ## Introduction | ## Introduction de [objet/section] |
| ## Conclusion | ## Conclusion de [objet/section] |

All Introduction and Conclusion titles must be at level `##`.

## Neutrality (strict)

**Remove or rewrite:**
- Auto-appreciation: "important", "majeur", "robuste", "rigoureux", "ambitieux"
- Editorial justification: "volontairement", "conservateur", "verrou", "discipline"
- Reader address: "le lecteur verra que…" → factual statement
- Introspection: "nous avons choisi…" → neutral formulation
- Meta-commentary on the text itself

**Use instead:**
- Factual: "On définit…", "On suppose…", "On montre…", "Il s'ensuit…"
- Structural references: "voir Chapitre X", "d'après la Proposition Y" (without evaluative terms)

## Transitions

- Replace "La continuation ainsi…" by content-driven transitions
- Each paragraph should follow from the mathematical content, not from meta-phrases
- Avoid "on poursuit de la même manière" without specifying what follows

## Hypotheses and results

- Before each lemma, proposition, theorem: state hypotheses explicitly
- In the proof: indicate when each hypothesis is used
- No implicit or "obvious" hypotheses

## References and citations

- Cite exact source (theorem, page, equation number)
- Avoid "il est bien connu que" without reference
- For overlap with literature: state the difference (hypotheses, framework) factually

## Quantifiers and domains

- Explicit quantifiers: "pour tout", "il existe", "il existe un unique" with clear domain
- Explicit domain of definition for functions and operators
- Validity conditions in the statement, not only in the proof

## Terminology

- One concept = one term throughout
- No fluctuating synonyms for the same object
- For long documents: recall local conventions at section start if needed

## Proofs

- No "il est facile de voir" or "on laisse au lecteur" without a precise pointer
- Either detail the argument or refer to a lemma/reference
- Long calculations: state the intermediate result, move details to appendix with reference

## Conjectures and open questions

- Neutral formulation: "On conjecture que…", "Il serait naturel de se demander si…"
- No overstatement of importance
- Limits of the framework: recall restrictive hypotheses in section conclusion if relevant

## Voice and tense

- Present atemporal for mathematical statements
- Uniform voice: either "on" or passive throughout
- Future only for explicit forward references ("on verra en 4.2 que…")

## Quick scan patterns

When scanning a chunk, flag:
- `## Introduction` or `## Conclusion` without "de …"
- "important", "majeur", "volontairement", "verrou", "discipline"
- "Le lecteur", "on laisse au lecteur", "il est facile de voir"
- "La continuation ainsi", "on poursuit de la même manière"
- "il est bien connu que" without citation