algo/.cursor/skills/document-improvement/reference.md

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