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algo/docs/collatz_run_report_2026-03-09_c2_projective.md
ncantu e3e68fe39c Formalize C2 and add deterministic projective verification artefacts 
**Motivations:**
- Make Lemma C2 assertions citeable without terminal transcripts
- Provide a deterministic check for “both-children residual” and projective projection to B12

**Root causes:**
- C2 relied on narrative links between completion docs and B12 invariance without a machine-checkable artefact

**Correctifs:**
- Add a deterministic verifier that checks set equalities and projections from the existing completion MD sources

**Evolutions:**
- Version C2 verification artefacts in docs/artefacts
- Add a run report profile (sha256 + metrics) for C2 projective verification
- Update the proof plan with explicit C2 statements and references

**Pages affectées:**
- applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py
- docs/artefacts/collatz/c2_projective/verification_c2_projective.json
- docs/artefacts/collatz/c2_projective/verification_c2_projective.md
- applications/collatz/collatz_k_scripts/collatz_generate_run_report.py
- docs/collatz_run_report_2026-03-09_c2_projective.md
- docs/collatz_run_report_format.md
- docs/features/collatz_run_report_generator.md
- docs/features/collatz_c2_projective_verification.md
- applications/collatz/collatz_k_scripts/plan_lemmes_manquants_et_programme_de_preuve.md
2026-03-09 01:25:16 +01:00

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Auteur : Équipe 4NK

Rapport d’exécution — c2_projective

Contexte

  • But du run : vérifier C2 (complétion par frères ⇒ both ⇒ projection B12) sur des artefacts déterministes.
  • Assertion vérifiée : égalités d’ensembles et égalité de projections modulo 4096 (voir métriques).

Code et reproductibilité

  • Commit Git : e12c544e7bf8d7a6f9518cdd4959d0da07bccc07
  • Commande :
python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py --profile c2_projective --scope c2_projective --out-dir applications/collatz/out --docs-dir docs --c2-artefacts-dir docs/artefacts/collatz/c2_projective

Empreintes sha256 (scripts, artefacts)

  • /home/ncantu/code/algo/applications/collatz/collatz_k_scripts/collatz_verify_c2_projective.py
    • sha256: 4f515d649c44c4ffe55349b07c72e9e766f591f7596e1bcdf0f9447e6b94950d
  • /home/ncantu/code/algo/applications/collatz/collatz_k_scripts/noyau_both_base_4096.md
    • sha256: d0abffeca9ce2356d13b31ee4325b68fd85cf061670a8524b8e60fd15aba881b
  • /home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md
    • sha256: acc8667be8e93a33fadf45bacd5cd788ec05089d844616cf1762330ac0d41d67
  • /home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md
    • sha256: 956f8fd19570b7614705384995b52b6bf81399ca8dc36c3ea33bcbad3e4aff50
  • /home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.json
    • sha256: b1b9ab9d5d4f9d4ee60e7efd43b853ac29d3d51a19c2d71bdac45c4340d01bf0
  • /home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.md
    • sha256: 8bd84cb2149d297487e0e0ff03ebe96ff27b07a5ab677407cb4b9a17a339c2ba

Compteurs et métriques

  • |B12| = 192
  • m=14: |both|=593, |children(m=15)|=1186, |listed residual(m=15)|=1186
  • m=14: children(m=15) == residual(m=15) : True
  • m=14: both mod 4096 == B12 : True
  • m=15: |both|=1101, |children(m=16)|=2202
  • m=15: both mod 4096 == B12 : True

Chemins d’artefacts (versionnés)

  • ARTEFACTS : /home/ncantu/code/algo/docs/artefacts/collatz/c2_projective