From 4a2f06c4be18ce8285049560ee375e425c1451b5 Mon Sep 17 00:00:00 2001 From: ncantu Date: Mon, 9 Mar 2026 02:08:28 +0100 Subject: [PATCH] =?UTF-8?q?collatz:=20add=20completion=20m16=E2=86=92m17?= =?UTF-8?q?=20to=20C2=20artefacts?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit **Motivations:** - Extend C2 multi-transition chain beyond m=16 - Keep deterministic C2 artefacts aligned with new completion docs **Root causes:** - No completion doc existed for m>16, so C2 verifier couldn’t include it **Correctifs:** - Add complétion_minorée_m16_vers_m17.md with exhaustive both(m=16) list and declared |R_17^comp| - Regenerate C2 deterministic artefacts and run report to include the new transition **Evolutions:** - None **Pages affectées:** - applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md - 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 --- .../complétion_minorée_m16_vers_m17.md | 178 ++++++++++++++++++ .../verification_c2_projective.json | 13 +- .../verification_c2_projective.md | 2 + ...atz_run_report_2026-03-09_c2_projective.md | 8 +- 4 files changed, 197 insertions(+), 4 deletions(-) create mode 100644 applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md diff --git a/applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md b/applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md new file mode 100644 index 0000000..5bd32b2 --- /dev/null +++ b/applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md @@ -0,0 +1,178 @@ +# Complétion par frères au palier 2^17 (m=16 → m=17) + +## Introduction + +Ce document prolonge le schéma (C2.1) « complétion par frères ⇒ résidu = enfants des both » sur la transition m=16 → m=17, en partant d’un noyau déjà complété au palier 2^16. + +L’entrée de cette transition est le résidu complété \(R_{16}^{\mathrm{comp}}\) obtenu à la transition précédente (voir `complétion_minorée_m15_vers_m16.md`). À ce stade, la transition m→m+1 est une montée de palier : chaque classe a exactement deux enfants au palier suivant. + +## Données de départ + +- Palier m=16 : \(|R_{16}^{\mathrm{comp}}| = 2202\) (résidus impairs modulo \(2^{16}=65536\)). +- Palier m=17 (montée de palier, avant ajout de clauses nouvelles stabilisées à \(2^{17}\)) : + \[ + |R_{17}^{\mathrm{comp}}| = 2\cdot|R_{16}^{\mathrm{comp}}| = 4404. + \] + +## Décomposition parents → enfants (m=16 → m=17) + +Pour un parent \(r\in R_{16}^{\mathrm{comp}}\), les deux enfants au palier suivant sont \(r\) et \(r+2^{16}\). + +Dans cette transition, on ne distingue pas de cas « one » : l’ensemble d’entrée est déjà défini comme le résidu *après* complétion « one » au palier 2^16, et la montée de palier conserve systématiquement les deux enfants. + +Ainsi : + +- Parents « one » (1 enfant survivant) : 0 +- Parents « both » (2 enfants survivants) : \(|B_{16}|=|R_{16}^{\mathrm{comp}}|=2202\) + +Vérification de cohérence : +\[ +|R_{17}^{\mathrm{comp}}| = 2\cdot|B_{16}| = 4404. +\] + +## Résultat (déclaration de taille) + +|R_17^comp| = 2*|both| = 4404 + +## Listes exhaustives + +### Parents « both » au palier 2^16 (2202 résidus modulo 65536) + +27, 31, 47, 63, 71, 91, 103, 111, 159, 167, 223, 239, 251, 283, 319, 327 +359, 447, 479, 495, 511, 559, 603, 639, 667, 671, 703, 743, 751, 763, 767, 795 +859, 871, 895, 927, 959, 991, 1007, 1023, 1051, 1055, 1115, 1127, 1179, 1183, 1255, 1263 +1279, 1307, 1343, 1383, 1407, 1439, 1471, 1503, 1519, 1535, 1583, 1639, 1663, 1691, 1695, 1767 +1791, 1819, 1883, 1895, 1919, 1951, 1959, 2043, 2047, 2111, 2139, 2151, 2159, 2175, 2207, 2215 +2287, 2367, 2375, 2407, 2463, 2495, 2527, 2543, 2559, 2651, 2671, 2687, 2715, 2751, 2791, 2811 +2843, 2879, 2887, 2919, 2943, 3007, 3055, 3071, 3099, 3103, 3175, 3183, 3199, 3227, 3231, 3263 +3311, 3323, 3327, 3355, 3375, 3391, 3399, 3431, 3487, 3519, 3567, 3583, 3615, 3631, 3711, 3739 +3775, 3815, 3823, 3839, 3867, 3931, 3943, 3999, 4095, 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64543, 64575, 64615, 64623, 64639, 64671, 64679, 64703, 64751, 64763 +64767, 64795, 64815, 64831, 64871, 64895, 64927, 64959, 64991, 65023, 65051, 65055, 65071, 65127, 65151, 65183 +65215, 65263, 65279, 65307, 65383, 65407, 65471, 65519, 65531, 65535 diff --git a/docs/artefacts/collatz/c2_projective/verification_c2_projective.json b/docs/artefacts/collatz/c2_projective/verification_c2_projective.json index 53884d9..ac6931a 100644 --- a/docs/artefacts/collatz/c2_projective/verification_c2_projective.json +++ b/docs/artefacts/collatz/c2_projective/verification_c2_projective.json @@ -3,7 +3,8 @@ "noyau_both_base_4096_md": "applications/collatz/collatz_k_scripts/noyau_both_base_4096.md", "completion_docs": [ "applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md", - "applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md" + "applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md", + "applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md" ] }, "B12": { @@ -31,6 +32,16 @@ "listed_residual_count": 2202, "children_equals_listed_residual": null, "projection_mod_4096_equals_b12": true + }, + { + "source": "applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md", + "palier_parent": 16, + "palier_child": 17, + "both_parent_count": 2202, + "computed_children_count": 4404, + "listed_residual_count": 4404, + "children_equals_listed_residual": null, + "projection_mod_4096_equals_b12": true } ], "checks": { diff --git a/docs/artefacts/collatz/c2_projective/verification_c2_projective.md b/docs/artefacts/collatz/c2_projective/verification_c2_projective.md index d0e7098..d21925c 100644 --- a/docs/artefacts/collatz/c2_projective/verification_c2_projective.md +++ b/docs/artefacts/collatz/c2_projective/verification_c2_projective.md @@ -7,6 +7,7 @@ - `noyau_both_base_4096.md` : `applications/collatz/collatz_k_scripts/noyau_both_base_4096.md` - completion : `applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md` - completion : `applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md` +- completion : `applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md` ## Base projective B12 @@ -19,6 +20,7 @@ | --- | --- | --- | --- | --- | --- | --- | --- | | applications/collatz/collatz_k_scripts/complétion_minorée_m14_vers_m15.md | 14 | 15 | 593 | 1186 | 1186 | True | True | | applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md | 15 | 16 | 1101 | 2202 | 2202 | | True | +| applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md | 16 | 17 | 2202 | 4404 | 4404 | | True | ## Sorties diff --git a/docs/collatz_run_report_2026-03-09_c2_projective.md b/docs/collatz_run_report_2026-03-09_c2_projective.md index 48f9951..e35864b 100644 --- a/docs/collatz_run_report_2026-03-09_c2_projective.md +++ b/docs/collatz_run_report_2026-03-09_c2_projective.md @@ -9,7 +9,7 @@ ## Code et reproductibilité -- **Commit Git** : `071da20b190207aebcbbbaad8e57b9e21b8282c6` +- **Commit Git** : `ace28bbecf9c9c768ed124ffe1dcd36aada5425a` - **Commande** : ```bash @@ -26,10 +26,12 @@ python3 applications/collatz/collatz_k_scripts/collatz_generate_run_report.py -- - sha256: `acc8667be8e93a33fadf45bacd5cd788ec05089d844616cf1762330ac0d41d67` - `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m15_vers_m16.md` - sha256: `956f8fd19570b7614705384995b52b6bf81399ca8dc36c3ea33bcbad3e4aff50` +- `/home/ncantu/code/algo/applications/collatz/collatz_k_scripts/complétion_minorée_m16_vers_m17.md` + - sha256: `b344d0af34508ca7bf59486f2b7b52c84a2dda46063155ed1f32e6652b22b7ca` - `/home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.json` - - sha256: `3f5ee61f259c90138d7c9fd3e8a2331947a2e25988bea349f246ad90fb1e43ec` + - sha256: `90f9f5f7481f438e73e05badf13dd22065f845b3d1efb7d43f4d0aa576fccd3c` - `/home/ncantu/code/algo/docs/artefacts/collatz/c2_projective/verification_c2_projective.md` - - sha256: `f4f5e00365ec6cc2253f2ef80ca51414d4ad79dc51bc0a408ff1bb352eba39f5` + - sha256: `c8b35eb6d9b7231d791a87b56f3343f0a4c5027f2d57ae13276ef3341819834d` ## Compteurs et métriques