ncantu 949886bb22 Collatz: align proof texts with artefacts (hybrid path)

**Motivations:**
- Keep Collatz proof documents citable and logically consistent with repository artefacts

**Root causes:**
- Run transcript and discussion pasted into proof text
- Global closure stated as fact without explicit discharge of H_ext(M)

**Correctifs:**
- Remove pasted transcript from conjoncture_collatz.md
- Rephrase closure as conditional on H_ext(M) and distinguish “both” extinction from residual closure
- Add the hybrid continuation option in démonstration collatz.md

**Evolutions:**
- Add fixKnowledge entry documenting the issue and remediation

**Pages affectées:**
- applications/collatz/conjoncture_collatz.md
- applications/collatz/démonstration collatz.md
- docs/fixKnowledge/collatz_docs_status_and_transcript_cleanup.md

2026-03-08 23:38:46 +01:00

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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.
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
docs/fixKnowledge/collatz_docs_status_and_transcript_cleanup.md

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