c29bbaec4b
**Motivations:**
- Make C2 verification robust when completion documents provide counts instead of full residual lists
- Prepare the verifier to support additional completion transitions with the same artefact structure
**Root causes:**
- m=15→m=16 completion doc may omit residual list and only state |R_16^comp| = 2*|both| = 2202
**Correctifs:**
- Parse and validate declared |R_{m+1}^comp| size when present
- Add generic transition discovery output in verification JSON
**Evolutions:**
- Regenerate versioned C2 verification artefacts and run report
**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
- docs/collatz_run_report_2026-03-09_c2_projective.md
1.2 KiB
1.2 KiB
Auteur : Équipe 4NK
Vérification déterministe — Lemma C2 (réduction projective)
Entrées
noyau_both_base_4096.md:applications/collatz/collatz_k_scripts/noyau_both_base_4096.mdcomplétion_minorée_m14_vers_m15.md:applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.mdcomplétion_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|)
- |listed residual (m=16)| : 2202
- 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