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algo/docs/artefacts/collatz/c2_projective/verification_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

Vérification déterministe — Lemma C2 (réduction projective)

Entrées

  • noyau_both_base_4096.md : applications/collatz/collatz_k_scripts/noyau_both_base_4096.md
  • complétion_minorée_m14_vers_m15.md : applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md
  • complétion_minorée_m15_vers_m16.md : applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md

Base projective B12

  • |B12| = 192 (attendu 192)
  • min(B12) = 27, max(B12) = 4095

Transition m=14 → m=15 (complétion par frères ⇒ résidu = enfants des both)

  • |both parents (m=14)| = 593
  • |computed children (m=15)| = 1186 (attendu 2*|both|)
  • |listed residual (m=15)| = 1186
  • computed children == listed residual : True
  • projection both(m=14) mod 4096 == B12 : True

Transition m=15 → m=16 (projection des both)

  • |both parents (m=15)| = 1101
  • |computed children (m=16)| = 2202 (attendu 2*|both|)
  • projection both(m=15) mod 4096 == B12 : True

Sorties

  • JSON : docs/artefacts/collatz/c2_projective/verification_c2_projective.json
  • Markdown : docs/artefacts/collatz/c2_projective/verification_c2_projective.md