**Motivations :**
- Align the manuscript structure with the scientific writing guide.
- Keep a single formalized proof-oriented header section in the document.
**Root causes :**
- The manuscript accumulated duplicated and mixed drafting layers over time.
- Scientific and conversational fragments were interleaved in the same file.
**Correctifs :**
- Added a normalized scientific section at the beginning of `v0/conjoncture_collatz.md`.
- Reintroduced explicit hypotheses, statement status, indexed quantitative results, and protocols.
**Evolutions :**
- Standardized theorem/lemma phrasing and section naming for research-style consistency.
**Pages affectées :**
- v0/conjoncture_collatz.md