Nicolas Cantu
a3827b20c2
**Motivations:** - Persist the current manuscript progress before push. - Keep audit artifacts and demonstration updates synchronized. **Root causes:** - New analytical materials were produced across multiple markdown files. - The demonstration file had both staged and unstaged edits needing consolidation. **Correctifs:** - Consolidated all pending markdown changes into a single coherent commit. - Included the updated demonstration text and the new extraction document. **Evolutions:** - Added full 60-state audit content for the B12 projective core at modulo 4096. - Added dedicated extraction notes for analytical resolution at step 8. - Added projective base reference for the "both" core. **Pages affectées:** - v0/audit_60_etats_B12_mod4096_horizon7.md - v0/démonstration collatz.md - v0/noyau_both_base_4096.md - v0/extraction analytique_60états.md
52 lines
2.3 KiB
Markdown
52 lines
2.3 KiB
Markdown
# Noyau « both » et base projective au module 4096
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## Résumé
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Ce document formalise une réduction structurale obtenue par la stratégie de complétion par frères :
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- à chaque transition m → m+1, les cas « one » sont fermables par clauses de descente minorées ;
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- le résidu restant est engendré uniquement par les parents « both » ;
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- à partir de m=12, l’ensemble des parents « both » réduit modulo 4096 vers une base fixe B_12 de 192 résidus.
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## Cardinaux (registre exact)
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| m | |R_m| | |B_m| (parents both) | q_m^comp = |B_m|/|R_m| |
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|---:|---:|---:|---:|
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| 11 | 134 | 102 | 0.7611940298507462 |
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| 12 | 236 | 192 | 0.8135593220338984 |
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| 13 | 428 | 324 | 0.7570093457943925 |
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| 14 | 752 | 593 | 0.7885638297872340 |
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| 15 | 1345 | 1101 | 0.8185873605947955 |
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## Invariance projective au module 4096
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Vérification : B_13 mod 4096 = B_12, B_14 mod 4096 = B_12, B_15 mod 4096 = B_12.
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## Multiplicités de relèvement (nombre de lifts par résidu de la base)
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Relèvement B_12 → B_13 (mod 4096 → mod 8192) :
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- 1 lift(s) : 60
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- 2 lift(s) : 132
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Relèvement B_13 → B_14 (mod 8192 → mod 16384) :
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- 1 lift(s) : 55
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- 2 lift(s) : 269
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Relèvement B_14 → B_15 (mod 16384 → mod 32768) :
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- 1 lift(s) : 85
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- 2 lift(s) : 508
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## Base projective B_12 (192 résidus impairs modulo 4096)
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27, 31, 47, 63, 71, 91, 103, 111, 127, 159, 167, 191, 223, 239, 251, 255
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283, 303, 319, 327, 359, 415, 447, 479, 495, 511, 539, 559, 603, 623, 639, 667
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671, 679, 703, 743, 751, 763, 767, 795, 831, 839, 859, 871, 895, 927, 959, 991
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1007, 1023, 1051, 1055, 1095, 1115, 1127, 1135, 1151, 1179, 1183, 1191, 1215, 1247, 1255, 1263
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1275, 1279, 1307, 1327, 1343, 1351, 1383, 1407, 1439, 1471, 1503, 1519, 1535, 1563, 1567, 1583
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1639, 1663, 1691, 1695, 1727, 1767, 1775, 1791, 1819, 1883, 1895, 1919, 1951, 1959, 1983, 2043
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2047, 2075, 2079, 2095, 2111, 2119, 2139, 2151, 2159, 2175, 2207, 2215, 2271, 2287, 2299, 2303
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2331, 2367, 2375, 2407, 2463, 2495, 2527, 2543, 2559, 2607, 2651, 2663, 2671, 2687, 2715, 2719
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2727, 2751, 2791, 2799, 2811, 2815, 2843, 2879, 2887, 2919, 2943, 2983, 3007, 3039, 3055, 3067
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3071, 3099, 3103, 3135, 3163, 3175, 3183, 3199, 3227, 3231, 3239, 3263, 3303, 3311, 3323, 3327
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3355, 3375, 3391, 3399, 3431, 3455, 3487, 3519, 3551, 3567, 3583, 3611, 3615, 3631, 3687, 3711
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3739, 3743, 3775, 3815, 3823, 3839, 3867, 3931, 3943, 3967, 3999, 4007, 4031, 4079, 4091, 4095
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