diff --git a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed-Csharp.ipynb b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed-Csharp.ipynb
index 1ee2085498..1810b37571 100644
--- a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed-Csharp.ipynb
+++ b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed-Csharp.ipynb
@@ -25,7 +25,7 @@
     "La recherche informée exploite une connaissance du problème — une **heuristique** $h(n)$ qui estime le coût restant vers le but — pour guider l'exploration vers les régions prometteuses de l'espace. Ce notebook montre, en C#, comment chaque algorithme combine différemment le coût déjà accumulé $g(n)$ et l'estimation $h(n)$ :\n",
     "\n",
     "- **Greedy Best-First** : fonce vers le but en minimisant $h(n)$ seul — rapide mais **sous-optimal**.\n",
-    "- **A\\*** : équilibre $f(n) = g(n) + h(n)$ — **optimal** si $h$ est admissible.\n",
+    "- **A\\*** : équilibre $f(n) = g(n) + h(n)$ — **optimal** si $h$ est consistante (la variante Graph-Search implémentée ici ne ré-ouvre pas les états fermés ; contre-exemple à quatre nœuds : jumeau Python §6).\n",
     "- **IDA\\*** : A* à approfondissement itéré par borne sur $f$ — optimal et **borné en mémoire** $O(bd)$.\n",
     "\n",
     "### Objectifs d'apprentissage\n",
@@ -846,7 +846,7 @@
     "| Optimalité | **Oui** | si $h$ **consistante** (et Graph-Search, pas de re-open) |\n",
     "| Mémoire | $O(b^d)$ | exponentielle |\n",
     "\n",
-    "> **Théorème (Hart, Nilsson, Raphael 1968)** : si $h$ est admissible, A* trouve un chemin de coût minimal."
+    "> **Théorème (Hart, Nilsson, Raphael 1968)** : si $h$ est admissible, A* trouve un chemin de coût minimal — à condition de **ré-ouvrir** un état fermé quand un meilleur $g$ arrive. La variante Graph-Search **sans ré-ouverture** de ce notebook exige $h$ **consistante** (contre-exemple à quatre nœuds : jumeau Python §6)."
    ]
   },
   {
@@ -1956,7 +1956,7 @@
     "|----------|--------|\n",
     "| **Mémoire** | $O(bd)$ — linéaire en profondeur (vs $O(b^d)$ pour A*) |\n",
     "| **Pas de file de priorité** | DFS récursif simple |\n",
-    "| **Même optimalité** | A* avec la même heuristique admissible |\n",
+    "| **Même optimalité** | que A* ; $h$ admissible suffit à IDA* (pas d'ensemble fermé), la variante A* sans re-open exige $h$ consistante |\n",
     "\n",
     "**Inconvénient** : re-exploration des nœuds à chaque itération (comme IDDFS), mais l'overhead est modeste car la borne $f$ augmente peu à chaque cycle."
    ]
@@ -2247,7 +2247,7 @@
     "\n",
     "| Heuristique | Définition | Admissible ? | Consistante ? |\n",
     "|-------------|------------|--------------|---------------|\n",
-    "| **$h_1$ Tuiles mal placées** | Nombre de tuiles hors de leur position but | Oui | Pas toujours |\n",
+    "| **$h_1$ Tuiles mal placées** (case vide exclue) | Nombre de tuiles hors de leur position but | Oui | **Oui** (un mouvement déplace une seule tuile numérotée) |\n",
     "| **$h_2$ Distance Manhattan** | Somme des distances $L_1$ de chaque tuile à sa position but | Oui | **Oui** |\n",
     "\n",
     "De plus, $h_2$ **domine** $h_1$ : $h_2(n) \\geq h_1(n)$ partout — donc A* avec $h_2$ explore **au moins aussi peu** de nœuds qu'avec $h_1$."
@@ -2830,13 +2830,13 @@
     "| Algorithme | Critère | Optimal | Mémoire | Quand ? |\n",
     "|------------|---------|---------|---------|---------|\n",
     "| **Greedy** | minimiser $h(n)$ | Non | $O(b^m)$ | Vitesse prioritaire, solution « assez bonne » |\n",
-    "| **A\\*** | minimiser $g(n) + h(n)$ | **Oui** (h admissible) | $O(b^d)$ | Référence, optimalité requise |\n",
+    "| **A\\*** | minimiser $g(n) + h(n)$ | **Oui** (h consistante, variante sans re-open) | $O(b^d)$ | Référence, optimalité requise |\n",
     "| **IDA\\*** | DFS itéré par $f(n)$ | **Oui** | $O(bd)$ | Mémoire limitée, espace profond |\n",
     "\n",
     "### Ce qu'il faut retenir\n",
     "\n",
     "1. **Greedy vs A* sur Lille → Toulouse** : Greedy (1210 km) est ~14% sous-optimal vs A* (1055 km) — la divergence est **structurelle**, pas accidentelle.\n",
-    "2. **A* est l'algorithme de référence** : optimal avec heuristique admissible, c'est le choix par défaut.\n",
+    "2. **A* est l'algorithme de référence** : optimal avec heuristique consistante (admissible seule ne suffit pas sans ré-ouverture), c'est le choix par défaut.\n",
     "3. **IDA* pour la mémoire** : même optimalité qu'A*, consommation **linéaire** au lieu d'exponentielle.\n",
     "4. **La qualité de l'heuristique est déterminante** : Manhattan (consistante, dominante) explore bien moins de nœuds que « tuiles mal placées » sur le 8-puzzle.\n",
     "\n",
diff --git a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb
index 66df05d826..262eb2daab 100644
--- a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb
+++ b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb
@@ -5,10 +5,10 @@
    "id": "nav-header",
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@@ -40,16 +40,16 @@
    "id": "imports",
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@@ -95,10 +95,10 @@
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@@ -147,10 +147,10 @@
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@@ -169,16 +169,16 @@
    "id": "node-class",
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@@ -333,10 +333,10 @@
    "id": "problem-example-intro",
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@@ -353,16 +353,16 @@
    "id": "graph-problem",
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+     "iopub.execute_input": "2026-09-06T22:12:22.119976Z",
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@@ -442,10 +442,10 @@
    "id": "heuristic-intro",
    "metadata": {
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@@ -465,16 +465,16 @@
    "id": "heuristic-function",
    "metadata": {
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@@ -534,10 +534,10 @@
    "id": "greedy-section",
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@@ -571,16 +571,16 @@
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@@ -670,10 +670,10 @@
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@@ -688,16 +688,16 @@
    "id": "greedy-test",
    "metadata": {
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@@ -719,7 +719,7 @@
       "  Noeuds explores  : 2\n",
       "  Noeuds generes   : 8\n",
       "  Frontiere max    : 5\n",
-      "  Temps            : 0.06 ms\n"
+      "  Temps            : 0.10 ms\n"
      ]
     }
    ],
@@ -737,10 +737,10 @@
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@@ -767,10 +767,10 @@
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@@ -797,10 +797,10 @@
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@@ -848,16 +848,16 @@
    "id": "astar-impl",
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@@ -950,10 +950,10 @@
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@@ -968,16 +968,16 @@
    "id": "astar-test",
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@@ -1018,10 +1018,10 @@
    "id": "1mddry1upc6",
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@@ -1030,7 +1030,7 @@
     "***\n",
     "### Test de l'algorithme A*\n",
     "\n",
-    "L'algorithme **A\\*** (A-Star) est l'un des algorithmes de recherche les plus utilisés en IA. Il garantit de trouver le chemin optimal si l'heuristique est **admissible** (ne surestime jamais le coût réel).\n",
+    "L'algorithme **A\\*** (A-Star) est l'un des algorithmes de recherche les plus utilisés en IA. Il garantit de trouver le chemin optimal si l'heuristique est **consistante** (ne surestime jamais le coût réel et ne diminue pas plus vite que le coût des arcs) — la condition qui correspond à la variante Graph-Search implémentée ici, qui ne ré-ouvre jamais un état fermé (contre-exemple avec une heuristique seulement admissible : §6).\n",
     "\n",
     "**Fonction d'évaluation** : `f(n) = g(n) + h(n)`\n",
     "- `g(n)` : coût du chemin depuis le départ\n",
@@ -1045,10 +1045,10 @@
    "id": "astar-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.009003,
-     "end_time": "2026-08-23T03:34:46.104649",
+     "duration": 0.007247,
+     "end_time": "2026-09-06T22:12:22.353638",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.095646",
+     "start_time": "2026-09-06T22:12:22.346391",
      "status": "completed"
     },
     "tags": []
@@ -1074,10 +1074,10 @@
    "id": "comparison-section",
    "metadata": {
     "papermill": {
-     "duration": 0.008974,
-     "end_time": "2026-08-23T03:34:46.120244",
+     "duration": 0.007098,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.111270",
+     "start_time": "2026-09-06T22:12:22.360937",
      "status": "completed"
     },
     "tags": []
@@ -1094,16 +1094,16 @@
    "id": "comparison-greedy-astar",
    "metadata": {
     "execution": {
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-     "iopub.status.busy": "2026-08-23T03:34:46.133860Z",
-     "iopub.status.idle": "2026-08-23T03:34:46.146191Z",
-     "shell.execute_reply": "2026-08-23T03:34:46.145668Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.382607Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.382607Z",
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     },
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-     "end_time": "2026-08-23T03:34:46.147228",
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.126328",
+     "start_time": "2026-09-06T22:12:22.375256",
      "status": "completed"
     },
     "tags": []
@@ -1116,7 +1116,7 @@
       "Comparaison : Greedy vs A*\n",
       "======================================================================\n",
       "Algorithme                          Chemin  Cout (km)  Longueur  Noeuds explores Temps (ms)\n",
-      "    Greedy Bordeaux -> Paris -> Strasbourg       1075         2                2       0.04\n",
+      "    Greedy Bordeaux -> Paris -> Strasbourg       1075         2                2       0.03\n",
       "        A* Bordeaux -> Paris -> Strasbourg       1075         2                3       0.02\n",
       "\n",
       "======================================================================\n",
@@ -1172,10 +1172,10 @@
    "id": "6ab7895c",
    "metadata": {
     "papermill": {
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-     "end_time": "2026-08-23T03:34:46.160360",
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      "exception": false,
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+     "start_time": "2026-09-06T22:12:22.411785",
      "status": "completed"
     },
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@@ -1201,16 +1201,16 @@
    "id": "ca315179",
    "metadata": {
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-     "shell.execute_reply": "2026-08-23T03:34:46.182867Z"
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-     "end_time": "2026-08-23T03:34:46.183873",
+     "duration": 0.016014,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.167928",
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      "status": "completed"
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@@ -1282,10 +1282,10 @@
    "id": "comparison-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.00653,
-     "end_time": "2026-08-23T03:34:46.196402",
+     "duration": 0.007021,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.189872",
+     "start_time": "2026-09-06T22:12:22.447844",
      "status": "completed"
     },
     "tags": []
@@ -1297,7 +1297,7 @@
     "\n",
     "| Aspect | Greedy | A* |\n",
     "|--------|--------|-----|\n",
-    "| Optimalité | Non garantie | Garantie (avec heuristique admissible) |\n",
+    "| Optimalité | Non garantie | Garantie (avec heuristique consistante) |\n",
     "| Nœuds explorés | Généralement moins | Peut être plus |\n",
     "| Qualité solution | Variable | Toujours optimale |\n",
     "\n",
@@ -1309,10 +1309,10 @@
    "id": "ida-section",
    "metadata": {
     "papermill": {
-     "duration": 0.006121,
-     "end_time": "2026-08-23T03:34:46.209502",
+     "duration": 0.006026,
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      "exception": false,
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+     "start_time": "2026-09-06T22:12:22.461606",
      "status": "completed"
     },
     "tags": []
@@ -1346,16 +1346,16 @@
    "id": "idastar-impl",
    "metadata": {
     "execution": {
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-     "shell.execute_reply": "2026-08-23T03:34:46.229592Z"
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-     "end_time": "2026-08-23T03:34:46.230659",
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.216196",
+     "start_time": "2026-09-06T22:12:22.474644",
      "status": "completed"
     },
     "tags": []
@@ -1449,10 +1449,10 @@
    "id": "40f8a8e5",
    "metadata": {
     "papermill": {
-     "duration": 0.005999,
-     "end_time": "2026-08-23T03:34:46.244341",
+     "duration": 0.007354,
+     "end_time": "2026-09-06T22:12:22.510632",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.238342",
+     "start_time": "2026-09-06T22:12:22.503278",
      "status": "completed"
     },
     "tags": []
@@ -1467,16 +1467,16 @@
    "id": "idastar-test",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:46.257373Z",
-     "iopub.status.busy": "2026-08-23T03:34:46.257373Z",
-     "iopub.status.idle": "2026-08-23T03:34:46.261068Z",
-     "shell.execute_reply": "2026-08-23T03:34:46.260588Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.535981Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.535981Z",
+     "iopub.status.idle": "2026-09-06T22:12:22.539492Z",
+     "shell.execute_reply": "2026-09-06T22:12:22.538964Z"
     },
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-     "end_time": "2026-08-23T03:34:46.261602",
+     "duration": 0.018523,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.250378",
+     "start_time": "2026-09-06T22:12:22.521490",
      "status": "completed"
     },
     "tags": []
@@ -1500,7 +1500,7 @@
       "  Noeuds explores  : 8\n",
       "  Noeuds generes   : 24\n",
       "  Frontiere max    : 4\n",
-      "  Temps            : 0.10 ms\n"
+      "  Temps            : 0.09 ms\n"
      ]
     }
    ],
@@ -1518,10 +1518,10 @@
    "id": "0gzwacp0hfbq",
    "metadata": {
     "papermill": {
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+     "start_time": "2026-09-06T22:12:22.546584",
      "status": "completed"
     },
     "tags": []
@@ -1545,10 +1545,10 @@
    "id": "idastar-interpretation",
    "metadata": {
     "papermill": {
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-     "end_time": "2026-08-23T03:34:46.283809",
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      "status": "completed"
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@@ -1576,10 +1576,10 @@
    "id": "752d920b",
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.289341",
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      "status": "completed"
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@@ -1605,16 +1605,16 @@
    "id": "b119ca90",
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-     "shell.execute_reply": "2026-08-23T03:34:46.310453Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.606986Z",
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      "status": "completed"
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@@ -1645,10 +1645,10 @@
    "id": "all-comparison-section",
    "metadata": {
     "papermill": {
-     "duration": 0.005504,
-     "end_time": "2026-08-23T03:34:46.323130",
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      "exception": false,
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      "status": "completed"
     },
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@@ -1665,16 +1665,16 @@
    "id": "all-comparison",
    "metadata": {
     "execution": {
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-     "iopub.status.idle": "2026-08-23T03:34:46.341236Z",
-     "shell.execute_reply": "2026-08-23T03:34:46.341236Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.641238Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.641238Z",
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-     "end_time": "2026-08-23T03:34:46.341236",
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.329196",
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      "status": "completed"
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@@ -1772,10 +1772,10 @@
    "id": "all-comparison-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.004999,
-     "end_time": "2026-08-23T03:34:46.353674",
+     "duration": 0.007517,
+     "end_time": "2026-09-06T22:12:22.663906",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.348675",
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      "status": "completed"
     },
     "tags": []
@@ -1804,10 +1804,10 @@
    "id": "heuristic-design-section",
    "metadata": {
     "papermill": {
-     "duration": 0.006018,
-     "end_time": "2026-08-23T03:34:46.365693",
+     "duration": 0.008347,
+     "end_time": "2026-09-06T22:12:22.678943",
      "exception": false,
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+     "start_time": "2026-09-06T22:12:22.670596",
      "status": "completed"
     },
     "tags": []
@@ -1823,10 +1823,10 @@
    "id": "admissibility-section",
    "metadata": {
     "papermill": {
-     "duration": 0.005546,
-     "end_time": "2026-08-23T03:34:46.377246",
+     "duration": 0.008249,
+     "end_time": "2026-09-06T22:12:22.693949",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.371700",
+     "start_time": "2026-09-06T22:12:22.685700",
      "status": "completed"
     },
     "tags": []
@@ -1847,7 +1847,9 @@
     "| Distance / 2 | Oui | Si l'heuristique originale est admissible, la diviser aussi |\n",
     "| Distance × 2 | Non | Peut surestimer le coût réel |\n",
     "\n",
-    "**Théorème** : A* avec une heuristique admissible est optimal (trouve une solution de coût minimal).\n"
+    "**Théorème** : A* avec une heuristique **consistante** est optimal (trouve une solution de coût minimal) — c'est la condition qui correspond à la variante Graph-Search implémentée dans ce notebook, qui ferme définitivement les états explorés.\n",
+    "\n",
+    "Avec une heuristique seulement **admissible**, la garantie d'optimalité exige une variante qui **ré-ouvre** un état fermé lorsqu'un meilleur $g$ arrive. Le contre-exemple ci-dessous le montre en pratique : une heuristique admissible partout, et pourtant un chemin sous-optimal.\n"
    ]
   },
   {
@@ -1855,10 +1857,10 @@
    "id": "consistency-section",
    "metadata": {
     "papermill": {
-     "duration": 0.006005,
-     "end_time": "2026-08-23T03:34:46.388384",
+     "duration": 0.00721,
+     "end_time": "2026-09-06T22:12:22.708102",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.382379",
+     "start_time": "2026-09-06T22:12:22.700892",
      "status": "completed"
     },
     "tags": []
@@ -1878,22 +1880,158 @@
     "|-----------|------------|-------------|\n",
     "| Définition | $h(n) \\leq h^*(n)$ | $h(n) \\leq c(n, n') + h(n')$ |\n",
     "| Relation | Consistante ⇒ Admissible | Admissible n'implique pas consistante |\n",
-    "| Effet sur A* | Optimalité | Optimalité + pas de *re-open* |\n",
+    "| Effet sur A* | Insuffisante pour cette variante (contre-exemple ci-dessous) | Optimalité + pas de *re-open* |\n",
     "\n",
     "**Exemple** : Pour le 8-puzzle :\n",
-    "- « Tuiles mal placées » est admissible mais pas nécessairement consistante\n",
+    "- « Tuiles mal placées » (**case vide exclue**) est admissible **et** consistante : un mouvement fait glisser une seule tuile numérotée, donc le compte varie d'au plus 1\n",
     "- « Distance Manhattan » est admissible **et** consistante\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "counterexample-intro",
+   "metadata": {
+    "papermill": {
+     "duration": 0.007448,
+     "end_time": "2026-09-06T22:12:22.723361",
+     "exception": false,
+     "start_time": "2026-09-06T22:12:22.715913",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "### Contre-exemple : admissible ne suffit pas (pour cette variante de A*)\n",
+    "\n",
+    "L'implémentation `a_star_search` (section 4) ferme définitivement chaque état exploré : un meilleur $g$ arrivant plus tard sur un état fermé est ignoré. Pour **cette** variante, la consistance est la condition qui **achète** l'optimalité — l'admissibilité seule ne suffit pas.\n",
+    "\n",
+    "Le graphe à quatre nœuds ci-dessous le démontre : l'heuristique est admissible **partout** (vérifiée exhaustivement contre $h^*$), deux arcs violent la consistance, et A* rend un chemin de coût **4** là où l'optimum est **3,5**.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "counterexample-demo",
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2026-09-06T22:12:22.738745Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.738745Z",
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+     "shell.execute_reply": "2026-09-06T22:12:22.746297Z"
+    },
+    "papermill": {
+     "duration": 0.016758,
+     "end_time": "2026-09-06T22:12:22.747604",
+     "exception": false,
+     "start_time": "2026-09-06T22:12:22.730846",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "admissible partout ? True   {'S': (3.5, 3.5), 'B': (2.5, 2.5), 'A': (0.0, 2.0), 'G': (0.0, 0.0)}\n",
+      "arcs violant la consistance : [('S', 'A', 'c=2.0', 'h(S)=3.5 > 2.0'), ('B', 'A', 'c=0.5', 'h(B)=2.5 > 0.5')]\n",
+      "A* du notebook          -> S -> A -> G 4.0\n",
+      "Optimum (Dijkstra/UCS)  -> S -> B -> A -> G 3.5\n",
+      "Ecart : A* rend 4.0 pour un optimum de 3.5 (14% de trop)\n"
+     ]
+    }
+   ],
+   "source": [
+    "# --- Contre-exemple : h admissible mais NON consistante -> A* (sans re-open) sous-optimal ---\n",
+    "\n",
+    "# Graphe oriente 4 noeuds. Optimum : S -> B -> A -> G = 1 + 0.5 + 2 = 3.5\n",
+    "counter_graph = {\n",
+    "    'S': {'A': 2.0, 'B': 1.0},\n",
+    "    'B': {'A': 0.5},\n",
+    "    'A': {'G': 2.0},\n",
+    "    'G': {},\n",
+    "}\n",
+    "\n",
+    "def h_inconsistent(state):\n",
+    "    \"\"\"h(S)=3.5, h(B)=2.5, h(A)=0, h(G)=0 : admissible partout, non consistante.\"\"\"\n",
+    "    return {'S': 3.5, 'B': 2.5, 'A': 0.0, 'G': 0.0}[state]\n",
+    "\n",
+    "def dijkstra_hstar(graph, goal):\n",
+    "    \"\"\"Couts optimaux exacts h*(n) vers le but (Dijkstra sur le graphe inverse).\"\"\"\n",
+    "    reverse = {n: {} for n in graph}\n",
+    "    for u, nbrs in graph.items():\n",
+    "        for v, c in nbrs.items():\n",
+    "            reverse.setdefault(v, {})[u] = c\n",
+    "    dist = {goal: 0.0}\n",
+    "    heap = [(0.0, goal)]\n",
+    "    while heap:\n",
+    "        d, u = heapq.heappop(heap)\n",
+    "        if d > dist.get(u, float('inf')):\n",
+    "            continue\n",
+    "        for v, c in reverse.get(u, {}).items():\n",
+    "            nd = d + c\n",
+    "            if nd < dist.get(v, float('inf')):\n",
+    "                dist[v] = nd\n",
+    "                heapq.heappush(heap, (nd, v))\n",
+    "    return dist\n",
+    "\n",
+    "h_star = dijkstra_hstar(counter_graph, 'G')\n",
+    "\n",
+    "# 1) Admissibilite : verifiee EXHAUSTIVEMENT sur les 4 etats (pas un echantillon)\n",
+    "adm = {n: h_inconsistent(n) <= h_star[n] for n in counter_graph}\n",
+    "print(\"admissible partout ?\", all(adm.values()),\n",
+    "      \" \", {n: (h_inconsistent(n), h_star[n]) for n in counter_graph})\n",
+    "\n",
+    "# 2) Consistance : les arcs qui violent h(n) <= c(n, n') + h(n')\n",
+    "violations = [\n",
+    "    (u, v, c) for u, nbrs in counter_graph.items() for v, c in nbrs.items()\n",
+    "    if h_inconsistent(u) > c + h_inconsistent(v)\n",
+    "]\n",
+    "print(\"arcs violant la consistance :\",\n",
+    "      [(u, v, f\"c={c}\", f\"h({u})={h_inconsistent(u)} > {c + h_inconsistent(v):.1f}\")\n",
+    "       for u, v, c in violations])\n",
+    "\n",
+    "# 3) A* du notebook (fermeture definitive) contre l'optimum Dijkstra/UCS\n",
+    "problem_ce = GraphProblem('S', 'G', counter_graph)\n",
+    "res_astar = a_star_search(problem_ce, h_inconsistent)\n",
+    "print(f\"A* du notebook          -> {' -> '.join(res_astar.path)} {res_astar.cost}\")\n",
+    "print(f\"Optimum (Dijkstra/UCS)  -> S -> B -> A -> G {h_star['S']}\")\n",
+    "print(f\"Ecart : A* rend {res_astar.cost} pour un optimum de {h_star['S']}\"\n",
+    "      f\" ({(res_astar.cost - h_star['S']) / h_star['S']:.0%} de trop)\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "counterexample-interpretation",
+   "metadata": {
+    "papermill": {
+     "duration": 0.008582,
+     "end_time": "2026-09-06T22:12:22.762933",
+     "exception": false,
+     "start_time": "2026-09-06T22:12:22.754351",
+     "status": "completed"
+    },
+    "tags": []
+   },
+   "source": [
+    "### Interprétation : pourquoi l'admissibilité ne suffit pas ici\n",
+    "\n",
+    "**Ce qui s'est passé** : A* développe S, puis A (f = 2), puis B (f = 3,5). Depuis B, un chemin de coût 1 + 0,5 = 1,5 vers A **améliorerait** le g de A (2 → 1,5) — mais A est déjà fermé, l'amélioration est ignorée. Le but est ensuite atteint via S → A → G de coût 4, alors que S → B → A → G coûte 3,5.\n",
+    "\n",
+    "**La leçon** : l'admissibilité ($h \\leq h^*$) garantit que $f$ ne sous-estime jamais le coût d'un chemin optimal passant par $n$ — mais un nœud fermé avec un $g$ non optimal ne revient jamais en frontière, et la garantie ne peut plus s'exercer. La consistance ($h(n) \\leq c(n, n') + h(n')$) maintient les $f$ monotones le long des chemins : le premier développement de chaque état est déjà optimal, ce qui rend la fermeture définitive **sans risque**.\n",
+    "\n",
+    "Ce contre-exemple est le **symétrique** de celui de la section 9 (exercice 2, #12465) : là, une heuristique **non admissible** rendait A* sous-optimal ; ici, l'heuristique est admissible **partout** et A* est sous-optimal quand même. Le couple forme la leçon complète : ce qui achète l'optimalité à **cette** variante de Graph-Search, c'est la **consistance**.\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "dominance-section",
    "metadata": {
     "papermill": {
-     "duration": 0.005524,
-     "end_time": "2026-08-23T03:34:46.398922",
+     "duration": 0.006699,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:46.393398",
+     "start_time": "2026-09-06T22:12:22.771287",
      "status": "completed"
     },
     "tags": []
@@ -1924,10 +2062,10 @@
    "id": "puzzle-section",
    "metadata": {
     "papermill": {
-     "duration": 0.005015,
-     "end_time": "2026-08-23T03:34:46.410522",
+     "duration": 0.007075,
+     "end_time": "2026-09-06T22:12:22.791959",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.405507",
+     "start_time": "2026-09-06T22:12:22.784884",
      "status": "completed"
     },
     "tags": []
@@ -1947,20 +2085,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 16,
    "id": "puzzle-class",
    "metadata": {
     "execution": {
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-     "iopub.status.idle": "2026-08-23T03:34:46.430276Z",
-     "shell.execute_reply": "2026-08-23T03:34:46.430276Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.807131Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.807131Z",
+     "iopub.status.idle": "2026-09-06T22:12:22.815784Z",
+     "shell.execute_reply": "2026-09-06T22:12:22.814950Z"
     },
     "papermill": {
-     "duration": 0.014766,
-     "end_time": "2026-08-23T03:34:46.431289",
+     "duration": 0.017268,
+     "end_time": "2026-09-06T22:12:22.815784",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.416523",
+     "start_time": "2026-09-06T22:12:22.798516",
      "status": "completed"
     },
     "tags": []
@@ -2098,10 +2236,10 @@
    "id": "b3189c7b",
    "metadata": {
     "papermill": {
-     "duration": 0.006004,
-     "end_time": "2026-08-23T03:34:46.443294",
+     "duration": 0.005637,
+     "end_time": "2026-09-06T22:12:22.828516",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.437290",
+     "start_time": "2026-09-06T22:12:22.822879",
      "status": "completed"
     },
     "tags": []
@@ -2112,20 +2250,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 17,
    "id": "puzzle-benchmark",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:46.456294Z",
-     "iopub.status.busy": "2026-08-23T03:34:46.455294Z",
-     "iopub.status.idle": "2026-08-23T03:34:47.884107Z",
-     "shell.execute_reply": "2026-08-23T03:34:47.883599Z"
+     "iopub.execute_input": "2026-09-06T22:12:22.843696Z",
+     "iopub.status.busy": "2026-09-06T22:12:22.843696Z",
+     "iopub.status.idle": "2026-09-06T22:12:24.518048Z",
+     "shell.execute_reply": "2026-09-06T22:12:24.518048Z"
     },
     "papermill": {
-     "duration": 1.435814,
-     "end_time": "2026-08-23T03:34:47.884107",
+     "duration": 1.683028,
+     "end_time": "2026-09-06T22:12:24.519062",
      "exception": false,
-     "start_time": "2026-08-23T03:34:46.448293",
+     "start_time": "2026-09-06T22:12:22.836034",
      "status": "completed"
     },
     "tags": []
@@ -2145,7 +2283,7 @@
       "\n",
       "Heuristique              Noeuds     Cout   Temps (ms)\n",
       "----------------------------------------------------------------------\n",
-      "Tuiles mal placees            1        1         0.03\n",
+      "Tuiles mal placees            1        1         0.02\n",
       "Distance Manhattan            1        1         0.01\n",
       "\n",
       "Reduction des noeuds explores : 0.0%\n",
@@ -2157,7 +2295,7 @@
       "\n",
       "Heuristique              Noeuds     Cout   Temps (ms)\n",
       "----------------------------------------------------------------------\n",
-      "Tuiles mal placees          770       16         4.33\n",
+      "Tuiles mal placees          770       16         4.46\n",
       "Distance Manhattan          220       16         1.52\n",
       "\n",
       "Reduction des noeuds explores : 71.4%\n",
@@ -2175,8 +2313,8 @@
       "\n",
       "Heuristique              Noeuds     Cout   Temps (ms)\n",
       "----------------------------------------------------------------------\n",
-      "Tuiles mal placees       143839       31      1143.01\n",
-      "Distance Manhattan        20290       31       251.84\n",
+      "Tuiles mal placees       143839       31      1414.71\n",
+      "Distance Manhattan        20290       31       223.80\n",
       "\n",
       "Reduction des noeuds explores : 85.9%\n"
      ]
@@ -2184,11 +2322,11 @@
     {
      "data": {
       "text/plain": [
-       "(<__main__.SearchResult at 0x13ac250fa10>,\n",
-       " <__main__.SearchResult at 0x13ac2051e50>)"
+       "(<__main__.SearchResult at 0x17867552610>,\n",
+       " <__main__.SearchResult at 0x17826fef550>)"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 17,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2237,10 +2375,10 @@
    "id": "k292t2mslp",
    "metadata": {
     "papermill": {
-     "duration": 0.006013,
-     "end_time": "2026-08-23T03:34:47.897126",
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      "exception": false,
-     "start_time": "2026-08-23T03:34:47.891113",
+     "start_time": "2026-09-06T22:12:24.526076",
      "status": "completed"
     },
     "tags": []
@@ -2265,10 +2403,10 @@
    "id": "puzzle-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.008305,
-     "end_time": "2026-08-23T03:34:47.911955",
+     "duration": 0.007024,
+     "end_time": "2026-09-06T22:12:24.547889",
      "exception": false,
-     "start_time": "2026-08-23T03:34:47.903650",
+     "start_time": "2026-09-06T22:12:24.540865",
      "status": "completed"
     },
     "tags": []
@@ -2296,10 +2434,10 @@
    "id": "d7b928ea",
    "metadata": {
     "papermill": {
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-     "end_time": "2026-08-23T03:34:47.924483",
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      "exception": false,
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+     "start_time": "2026-09-06T22:12:24.554891",
      "status": "completed"
     },
     "tags": []
@@ -2327,20 +2465,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 18,
    "id": "b55555ba",
    "metadata": {
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-     "shell.execute_reply": "2026-08-23T03:34:47.941092Z"
+     "iopub.execute_input": "2026-09-06T22:12:24.576823Z",
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     "papermill": {
-     "duration": 0.011291,
-     "end_time": "2026-08-23T03:34:47.942097",
+     "duration": 0.011791,
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      "exception": false,
-     "start_time": "2026-08-23T03:34:47.930806",
+     "start_time": "2026-09-06T22:12:24.569120",
      "status": "completed"
     },
     "tags": []
@@ -2374,10 +2512,10 @@
    "id": "visualization-section",
    "metadata": {
     "papermill": {
-     "duration": 0.008028,
-     "end_time": "2026-08-23T03:34:47.956124",
+     "duration": 0.014498,
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      "exception": false,
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      "status": "completed"
     },
     "tags": []
@@ -2390,20 +2528,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 19,
    "id": "puzzle-visualization",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:47.970129Z",
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-     "shell.execute_reply": "2026-08-23T03:34:48.266442Z"
+     "iopub.execute_input": "2026-09-06T22:12:24.636730Z",
+     "iopub.status.busy": "2026-09-06T22:12:24.636730Z",
+     "iopub.status.idle": "2026-09-06T22:12:24.988639Z",
+     "shell.execute_reply": "2026-09-06T22:12:24.988639Z"
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     "papermill": {
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-     "end_time": "2026-08-23T03:34:48.267977",
+     "duration": 0.369238,
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      "exception": false,
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      "status": "completed"
     },
     "tags": []
@@ -2525,10 +2663,10 @@
    "id": "visualization-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.006006,
-     "end_time": "2026-08-23T03:34:48.281022",
+     "duration": 0.00733,
+     "end_time": "2026-09-06T22:12:25.004914",
      "exception": false,
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+     "start_time": "2026-09-06T22:12:24.997584",
      "status": "completed"
     },
     "tags": []
@@ -2551,10 +2689,10 @@
    "id": "summary-table-section",
    "metadata": {
     "papermill": {
-     "duration": 0.006398,
-     "end_time": "2026-08-23T03:34:48.295559",
+     "duration": 0.006928,
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      "exception": false,
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      "status": "completed"
     },
     "tags": []
@@ -2567,20 +2705,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 20,
    "id": "final-comparison",
    "metadata": {
     "execution": {
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-     "shell.execute_reply": "2026-08-23T03:34:48.443041Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.035220Z",
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     },
     "papermill": {
-     "duration": 0.137514,
-     "end_time": "2026-08-23T03:34:48.444046",
+     "duration": 0.157151,
+     "end_time": "2026-09-06T22:12:25.184327",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.306532",
+     "start_time": "2026-09-06T22:12:25.027176",
      "status": "completed"
     },
     "tags": []
@@ -2765,10 +2903,10 @@
    "id": "summary-interpretation",
    "metadata": {
     "papermill": {
-     "duration": 0.007203,
-     "end_time": "2026-08-23T03:34:48.458251",
+     "duration": 0.008015,
+     "end_time": "2026-09-06T22:12:25.199346",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.451048",
+     "start_time": "2026-09-06T22:12:25.191331",
      "status": "completed"
     },
     "tags": []
@@ -2789,7 +2927,7 @@
     "| IDA* | Oui | Oui** | $f(n)$ itérée | Oui |\n",
     "\n",
     "\\* Optimal uniquement avec coûts uniformes.  \n",
-    "\\*\\* Optimal avec heuristique admissible.\n",
+    "\\*\\* A\\* : optimal avec heuristique **consistante** (variante Graph-Search sans ré-ouverture, contre-exemple §6) ; IDA\\* : optimal avec heuristique admissible (pas d'ensemble fermé).\n",
     "\n",
     "**Guide de choix pratique** :\n",
     "\n",
@@ -2807,10 +2945,10 @@
    "id": "exercises-section",
    "metadata": {
     "papermill": {
-     "duration": 0.006421,
-     "end_time": "2026-08-23T03:34:48.470673",
+     "duration": 0.008003,
+     "end_time": "2026-09-06T22:12:25.215917",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.464252",
+     "start_time": "2026-09-06T22:12:25.207914",
      "status": "completed"
     },
     "tags": []
@@ -2825,20 +2963,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 21,
    "id": "exercise1",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.485046Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.485046Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.488182Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.488182Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.233776Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.233776Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.236803Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.236803Z"
     },
     "papermill": {
-     "duration": 0.010348,
-     "end_time": "2026-08-23T03:34:48.488182",
+     "duration": 0.012372,
+     "end_time": "2026-09-06T22:12:25.236803",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.477834",
+     "start_time": "2026-09-06T22:12:25.224431",
      "status": "completed"
     },
     "tags": []
@@ -2861,10 +2999,10 @@
    "id": "exercise2",
    "metadata": {
     "papermill": {
-     "duration": 0.007526,
-     "end_time": "2026-08-23T03:34:48.501961",
+     "duration": 0.008231,
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      "exception": false,
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+     "start_time": "2026-09-06T22:12:25.244953",
      "status": "completed"
     },
     "tags": []
@@ -2877,20 +3015,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 22,
    "id": "exercise2-solution",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.515101Z",
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+     "iopub.execute_input": "2026-09-06T22:12:25.271147Z",
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     "papermill": {
-     "duration": 0.012725,
-     "end_time": "2026-08-23T03:34:48.520216",
+     "duration": 0.015712,
+     "end_time": "2026-09-06T22:12:25.277434",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.507491",
+     "start_time": "2026-09-06T22:12:25.261722",
      "status": "completed"
     },
     "tags": []
@@ -2963,10 +3101,10 @@
    "id": "afc1e48a",
    "metadata": {
     "papermill": {
-     "duration": 0.00612,
-     "end_time": "2026-08-23T03:34:48.534587",
+     "duration": 0.007998,
+     "end_time": "2026-09-06T22:12:25.293603",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.528467",
+     "start_time": "2026-09-06T22:12:25.285605",
      "status": "completed"
     },
     "tags": []
@@ -2985,20 +3123,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 23,
    "id": "6f576740",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.547595Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.547595Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.555533Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.555533Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.312531Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.311532Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.320079Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.320079Z"
     },
     "papermill": {
-     "duration": 0.015963,
-     "end_time": "2026-08-23T03:34:48.556550",
+     "duration": 0.018326,
+     "end_time": "2026-09-06T22:12:25.321092",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.540587",
+     "start_time": "2026-09-06T22:12:25.302766",
      "status": "completed"
     },
     "tags": []
@@ -3092,10 +3230,10 @@
    "id": "c36f7294",
    "metadata": {
     "papermill": {
-     "duration": 0.007,
-     "end_time": "2026-08-23T03:34:48.569984",
+     "duration": 0.008988,
+     "end_time": "2026-09-06T22:12:25.337128",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.562984",
+     "start_time": "2026-09-06T22:12:25.328140",
      "status": "completed"
     },
     "tags": []
@@ -3112,20 +3250,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 24,
    "id": "764c6b27",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.584513Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.583512Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.589689Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.589689Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.354238Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.354238Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.361736Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.361736Z"
     },
     "papermill": {
-     "duration": 0.014177,
-     "end_time": "2026-08-23T03:34:48.590705",
+     "duration": 0.017551,
+     "end_time": "2026-09-06T22:12:25.362746",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.576528",
+     "start_time": "2026-09-06T22:12:25.345195",
      "status": "completed"
     },
     "tags": []
@@ -3182,10 +3320,10 @@
    "id": "6ac45e53",
    "metadata": {
     "papermill": {
-     "duration": 0.006045,
-     "end_time": "2026-08-23T03:34:48.602346",
+     "duration": 0.008817,
+     "end_time": "2026-09-06T22:12:25.379078",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.596301",
+     "start_time": "2026-09-06T22:12:25.370261",
      "status": "completed"
     },
     "tags": []
@@ -3216,10 +3354,10 @@
    "id": "exercise3",
    "metadata": {
     "papermill": {
-     "duration": 0.007004,
-     "end_time": "2026-08-23T03:34:48.616610",
+     "duration": 0.008107,
+     "end_time": "2026-09-06T22:12:25.395252",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.609606",
+     "start_time": "2026-09-06T22:12:25.387145",
      "status": "completed"
     },
     "tags": []
@@ -3237,20 +3375,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 25,
    "id": "exercise3-solution",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.631854Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.630854Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.636799Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.636799Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.413040Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.412003Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.418286Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.418286Z"
     },
     "papermill": {
-     "duration": 0.014153,
-     "end_time": "2026-08-23T03:34:48.637857",
+     "duration": 0.016023,
+     "end_time": "2026-09-06T22:12:25.419299",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.623704",
+     "start_time": "2026-09-06T22:12:25.403276",
      "status": "completed"
     },
     "tags": []
@@ -3262,9 +3400,9 @@
      "text": [
       "Heuristique MST pour le TSP (sur le graphe des villes françaises)\n",
       "=================================================================\n",
-      "  current=Bordeaux     unvisited={'Marseille', 'Paris', 'Lyon'}                → h=1224 km\n",
-      "  current=Paris        unvisited={'Marseille', 'Nantes', 'Toulouse', 'Lyon'}   → h=1527 km\n",
-      "  current=Lyon         unvisited={'Nice', 'Grenoble'}                          → h=410 km\n",
+      "  current=Bordeaux     unvisited={'Lyon', 'Marseille', 'Paris'}                → h=1224 km\n",
+      "  current=Paris        unvisited={'Lyon', 'Marseille', 'Toulouse', 'Nantes'}   → h=1527 km\n",
+      "  current=Lyon         unvisited={'Grenoble', 'Nice'}                          → h=410 km\n",
       "\n",
       "Propriétés :\n",
       "  ✓ Admissible : le MST est une borne inférieure sur tout tour restant\n",
@@ -3358,10 +3496,10 @@
    "id": "exercise4",
    "metadata": {
     "papermill": {
-     "duration": 0.008002,
-     "end_time": "2026-08-23T03:34:48.652806",
+     "duration": 0.007059,
+     "end_time": "2026-09-06T22:12:25.434360",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.644804",
+     "start_time": "2026-09-06T22:12:25.427301",
      "status": "completed"
     },
     "tags": []
@@ -3376,20 +3514,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 26,
    "id": "exercise4-solution",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.668811Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.668811Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.741814Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.741814Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.452630Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.452630Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.526216Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.526216Z"
     },
     "papermill": {
-     "duration": 0.082006,
-     "end_time": "2026-08-23T03:34:48.741814",
+     "duration": 0.083635,
+     "end_time": "2026-09-06T22:12:25.527229",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.659808",
+     "start_time": "2026-09-06T22:12:25.443594",
      "status": "completed"
     },
     "tags": []
@@ -3552,10 +3690,10 @@
    "id": "97bc629e",
    "metadata": {
     "papermill": {
-     "duration": 0.007026,
-     "end_time": "2026-08-23T03:34:48.756194",
+     "duration": 0.007585,
+     "end_time": "2026-09-06T22:12:25.542429",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.749168",
+     "start_time": "2026-09-06T22:12:25.534844",
      "status": "completed"
     },
     "tags": []
@@ -3584,20 +3722,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 27,
    "id": "2a6adc42",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-23T03:34:48.771831Z",
-     "iopub.status.busy": "2026-08-23T03:34:48.770830Z",
-     "iopub.status.idle": "2026-08-23T03:34:48.776507Z",
-     "shell.execute_reply": "2026-08-23T03:34:48.776507Z"
+     "iopub.execute_input": "2026-09-06T22:12:25.558431Z",
+     "iopub.status.busy": "2026-09-06T22:12:25.558431Z",
+     "iopub.status.idle": "2026-09-06T22:12:25.563934Z",
+     "shell.execute_reply": "2026-09-06T22:12:25.563430Z"
     },
     "papermill": {
-     "duration": 0.012676,
-     "end_time": "2026-08-23T03:34:48.776507",
+     "duration": 0.015508,
+     "end_time": "2026-09-06T22:12:25.564939",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.763831",
+     "start_time": "2026-09-06T22:12:25.549431",
      "status": "completed"
     },
     "tags": []
@@ -3607,14 +3745,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Exercice 5 : implementez les TODO ci-dessus."
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n"
+      "Exercice 5 : implementez les TODO ci-dessus.\n"
      ]
     }
    ],
@@ -3694,10 +3825,10 @@
    "id": "conclusion-section",
    "metadata": {
     "papermill": {
-     "duration": 0.005998,
-     "end_time": "2026-08-23T03:34:48.790869",
+     "duration": 0.008165,
+     "end_time": "2026-09-06T22:12:25.582108",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.784871",
+     "start_time": "2026-09-06T22:12:25.573943",
      "status": "completed"
     },
     "tags": []
@@ -3720,13 +3851,13 @@
     "| Algorithme | Critère | Optimal | Mémoire |\n",
     "|------------|----------|---------|----------|\n",
     "| Greedy | Minimiser $h(n)$ | Non | $O(b^m)$ |\n",
-    "| A* | Minimiser $g(n) + h(n)$ | Oui (si $h$ admissible) | $O(b^d)$ |\n",
+    "| A* | Minimiser $g(n) + h(n)$ | Oui (si $h$ consistante) | $O(b^d)$ |\n",
     "| IDA* | DFS itéré par $f(n)$ | Oui | $O(bd)$ |\n",
     "\n",
     "### Ce qu'il faut retenir\n",
     "\n",
     "1. **L'heuristique est la clé** : une bonne heuristique peut réduire l'explosion combinatoire de plusieurs ordres de grandeur\n",
-    "2. **A* est l'algo de référence** : optimal avec heuristique admissible, utilisable dans la plupart des cas\n",
+    "2. **A* est l'algo de référence** : optimal avec heuristique consistante (admissible seule ne suffit pas sans ré-ouverture, cf §6), utilisable dans la plupart des cas\n",
     "3. **Greedy pour la vitesse** : quand une solution « assez bonne » suffit\n",
     "4. **IDA* pour la mémoire** : même optimalité que A*, avec une consommation linéaire\n",
     "5. **La dominance** : une heuristique plus informée (dominante) explore toujours moins de nœuds\n",
@@ -3747,10 +3878,10 @@
    "id": "nav-footer",
    "metadata": {
     "papermill": {
-     "duration": 0.00652,
-     "end_time": "2026-08-23T03:34:48.804936",
+     "duration": 0.009617,
+     "end_time": "2026-09-06T22:12:25.599994",
      "exception": false,
-     "start_time": "2026-08-23T03:34:48.798416",
+     "start_time": "2026-09-06T22:12:25.590377",
      "status": "completed"
     },
     "tags": []
@@ -3811,17 +3942,17 @@
   },
   "papermill": {
    "default_parameters": {},
-   "duration": 4.96378,
-   "end_time": "2026-08-23T03:34:49.165733",
+   "duration": 8.127561,
+   "end_time": "2026-09-06T22:12:25.969581",
    "environment_variables": {},
    "exception": null,
-   "input_path": "Search-03-Informed.ipynb",
-   "output_path": "12465_search3_exec.ipynb",
+   "input_path": "MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb",
+   "output_path": "MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03-Informed.ipynb",
    "parameters": {},
-   "start_time": "2026-08-23T03:34:44.201953",
+   "start_time": "2026-09-06T22:12:17.842020",
    "version": "2.6.0"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file
diff --git a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03d-WeightedAstar.ipynb b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03d-WeightedAstar.ipynb
index d4ed999f4e..ec9d88aaa9 100644
--- a/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03d-WeightedAstar.ipynb
+++ b/MyIA.AI.Notebooks/Search/Part1-Foundations/Search-03d-WeightedAstar.ipynb
@@ -17,7 +17,7 @@
     "## 1. L'idée : payer l'optimalité pour acheter de la vitesse\n",
     "\n",
     "[Search-3 (Informed)](../Part1-Foundations/Search-03-Informed.ipynb) a posé le\n",
-    "compromis fondateur : **A\\*** (admissible) est optimal mais peut explorer beaucoup\n",
+    "compromis fondateur : **A\\*** (heuristique consistante pour la variante sans ré-ouverture) est optimal mais peut explorer beaucoup\n",
     "de nœuds ; **Greedy** (sans `g`) est rapide mais peut renvoyer une solution\n",
     "carrément mauvaise. Entre l'optimalité chère et la gloutonnerie aveugle, existe-t-il\n",
     "un **juste milieu garanti** ?\n",
diff --git a/scripts/notebook_tools/twin_pairs.d/search-03-informed.yaml b/scripts/notebook_tools/twin_pairs.d/search-03-informed.yaml
index 625978d328..600a9e6dee 100644
--- a/scripts/notebook_tools/twin_pairs.d/search-03-informed.yaml
+++ b/scripts/notebook_tools/twin_pairs.d/search-03-informed.yaml
@@ -80,6 +80,13 @@
       csharp_sha: 1ee2085498a0d498b6ff3c975c2c0ef3e51b3833
       content_python_sha: e013f8349ff4a758216eb90f74e5dc8f926683738bdc8de50a4fa1cefd39c630
       content_csharp_sha: c3dfe1281305edc7800cb4b298751147ce76cc3c142b3886f41dac2a5da5dbca
+    - date: "2026-09-07"
+      by: myia-po-2026:CoursIA
+      python_sha: 262eb2daab28ef942cf281d8cf527a0ae200ae48
+      csharp_sha: 1810b37571f1cc28a8d7cce934cedee33328b469
+      content_python_sha: d76c6973ae30afa9730eedc02ca951184dd5a626684fdbbcf88e2f44e117a904
+      content_csharp_sha: 9266001db0b3b03023c359584137b11b9b93900aa45a641257ec0bd57ac6dc5b
+      reason: "PR #14824 (issue) : theoreme admissible=>optimal limite a la consistance (variante Graph-Search sans re-open). Python : enonces c19/c25/c38/c39/c54/c70 corriges + 3 cellules contre-exemple (graphe 4 noeuds, h admissible exhaustive, A* rend 4.0 vs optimum Dijkstra 3.5), re-exec papermill complete. C# : enonces c0/c9/c20/c24/c34 corriges (markdown-only, outputs precedents valides, pas de re-exec requis)."
   known_differences:
     - "Socle pedagogique commun : A* et Greedy Best-First avec differentes heuristiques (distance Manhattan, euclidienne, h=0=degenere en UCS). Arrive en Roumanie + 8-puzzle."
     - "Idiomes framework : Python = `import heapq` (priority queue avec (f, tie_breaker, noeud)). C# = `PriorityQueue<AStarNode, double>` (f-cost = g + h)."
diff --git a/scripts/notebook_tools/twin_pairs.d/search-14-weighted-a.yaml b/scripts/notebook_tools/twin_pairs.d/search-14-weighted-a.yaml
index 4a5e5efccb..52d88e7539 100644
--- a/scripts/notebook_tools/twin_pairs.d/search-14-weighted-a.yaml
+++ b/scripts/notebook_tools/twin_pairs.d/search-14-weighted-a.yaml
@@ -36,6 +36,13 @@
     csharp_sha: 31bfe385f948f0f69d3cda54067f73696607447d
     content_python_sha: 2adfd99c41d905a67d2093e6450151bcd2cb8cd373e0f5140676740c61626aff
     content_csharp_sha: d478f19b813a60e9da0fadd408ccb81e5055cec5f4108bd13cdb26350986349c
+  - date: "2026-09-07"
+    by: myia-po-2026:CoursIA
+    python_sha: ec9d88aaa9c3ed3eb3b0f12534e0c8b0d4d06636
+    csharp_sha: 31bfe385f948f0f69d3cda54067f73696607447d
+    content_python_sha: 9da03367b8539cc3ab4f15db67dacc44673b998593db12ff0347219536ce7592
+    content_csharp_sha: d478f19b813a60e9da0fadd408ccb81e5055cec5f4108bd13cdb26350986349c
+    reason: "PR #14824 (issue) : Search-03d c0 une ligne reconciliee (A* optimal exige h consistante pour la variante sans re-ouverture). Markdown-only, outputs precedents valides. C# 03d inchange : ses phrasings c3/c4 ('W=1 -> A* optimal, admissible') signales en residuel dans le body PR, hors enumeration de l'issue."
   bridge_verdict: SOTA-OK
   bridge_verdict_reason: 'Python = heapq (min-heap) + itertools.product + random.Random(seed), from-scratch. C# = PriorityQueue<T, double> (.NET 6+) + Random(seed), from-scratch. Verdict SOTA-OK (flip 2026-08-22, c.1301+335, myia-po-2025:CoursIA-2, issue #10382) : mislabel corrigige -- la reason anterieure concluat ''pedagogique from-scratch, pas de solveur tiers applicable'' (Weighted A* = algorithme pedagogique), qui contredit RECOVERABLE-LOCAL. Verifie firsthand : 3 imports Python / 1 using C#, aucun moteur tiers. Le balayage W sur f(n) = g(n) + W*h(n) est le sujet meme du chapitre ; PriorityQueue/heapq sont deja les primitives canoniques de leurs ecosystemes respectifs. From-scratch assumé des deux cotes, precedent GT-15 (PR #12312). parity_level preserve.'
   known_differences: