**Auteur** : Équipe 4NK

# Collatz docs: proof status and transcript cleanup

## Problem

Two Collatz documents mixed a mathematical narrative with an execution transcript (shell prompt + run logs + conversational text) and contained a logical mismatch:

- The text asserted a complete proof / total coverage / global threshold conclusion.
- The cited run excerpt reported a non-empty residual core at the audited final palier (e.g. `out/noyaux/noyau_post_D21.json` with a large number of residues).

This combination makes the documents non-citable as a proof document: conclusions are stated as established facts while the referenced artefacts do not discharge the required closure hypothesis.

## Root cause

- A run transcript and subsequent discussion were pasted directly into `applications/collatz/conjoncture_collatz.md`, after the conclusion section, without being moved to a dedicated log/report file.
- The wording in the conclusions did not keep the closure hypothesis explicit (extinction of the residual core \(R_M\)), and conflated partial extinction (e.g. “both” core) with global closure.

## Corrective actions

- Remove the pasted transcript from `applications/collatz/conjoncture_collatz.md` so the file remains a mathematical document.
- Requalify the end of `applications/collatz/conjoncture_collatz.md`:
  - keep “both” extinction as its own statement,
  - state global closure as conditional on an explicit hypothesis \(H_{\mathrm{ext}}(M): R_M=\varnothing\),
  - and document the selected continuation path (“hybrid”).
- Update `applications/collatz/démonstration collatz.md` to include the hybrid continuation option (certificate reduction + structural characterization + specific lemma) and keep the document conditionally correct.

## Impact

- The documents no longer contain a terminal transcript in the body of the proof text.
- Statements about global closure are now conditional on an explicit hypothesis, consistent with the run artefacts reported in the repository.

## Analysis modalities

- When a run transcript is needed, store it in a dedicated file (or in `out/` artefacts) and reference it from the proof document via a stable path and reproducible script invocation.
- Use the standard run report template in `docs/collatz_run_report_format.md`, and keep at least one concrete filled report in `docs/` for citation.
- For status checks, prefer referencing:
  - `applications/collatz/collatz_k_scripts/diagnostic_run_D18_D21_et_statut_preuve.md`
  - `applications/collatz/collatz_k_scripts/errata_demonstration_collatz.md`
  - `applications/collatz/collatz_k_scripts/plan_lemmes_manquants_et_programme_de_preuve.md`

## Deployment

No deployment. This change is documentation-only.

## Pages affected

- `applications/collatz/conjoncture_collatz.md`
- `applications/collatz/démonstration collatz.md`
- `applications/collatz/collatz_k_scripts/plan_lemmes_manquants_et_programme_de_preuve.md`
- `docs/fixKnowledge/collatz_docs_status_and_transcript_cleanup.md`
- `docs/collatz_run_report_format.md`
- `docs/collatz_run_report_2026-03-04_extend_D18_D21_resume_from_D20.md`