From 052805a8d78e73e4334feefea4a2e1043c32c6f5 Mon Sep 17 00:00:00 2001
From: jsboige <jsboige@gmail.com>
Date: Fri, 9 Oct 2026 17:19:07 +0200
Subject: [PATCH 1/3] fix(lean-11): retirer outputs/execution_count de la
 cellule markdown 3

La cellule 3 (markdown) portait des cles reservees aux cellules de code :
le carnet etait nbformat-invalide, ce qui empechait toute ecriture par un
editeur validant le schema (MCP jupyter-papermill). Motif rare dans la
famille Lean : 1 cellule sur 92 carnets, 3 carnets concernes.

See #17357

Co-Authored-By: Claude Haiku 4.5 (1M context) <noreply@anthropic.com>
---
 MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb | 2 --
 1 file changed, 2 deletions(-)

diff --git a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
index 29d5558e22..0153fe445b 100644
--- a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
+++ b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
@@ -325,7 +325,6 @@
   },
   {
    "cell_type": "markdown",
-   "execution_count": null,
    "id": "import-torchlean",
    "metadata": {
     "papermill": {
@@ -337,7 +336,6 @@
     },
     "tags": []
    },
-   "outputs": [],
    "source": [
     "### 2.4 Modules TorchLean — État du projet\n",
     "\n",

From 72172385610078ddcf95081f4161148348a972b9 Mon Sep 17 00:00:00 2001
From: jsboige <jsboige@gmail.com>
Date: Fri, 9 Oct 2026 17:39:20 +0200
Subject: [PATCH 2/3] fix(lean,#17357): Lean-11 TorchLean -- structure de
 sections, fuites de solution, re-exec
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Sept constats de l'audit #17073 (commentaire 5844023039) re-verifies firsthand
contre main, tous CONFIRMES :

- F1/F2/F3 : commentaires « solution attendue » sur les trois exercices, tous
  FAUX (la sortie imprime 0.0/0.0 la ou le commentaire annoncait 4.0, 7, 2.1,
  2.5) -- supprimes ; la sortie reste, elle est le vrai resultat du stub.
- F4 : en-tetes orphelins « 5.4 » et « 5.5 » dupliques, sans corps.
- F5 : section 3 ouverte deux fois (ancre 3-api en double).
- F6 : conclusion 8.x et ligne de navigation enterrees dans la cellule
  d'exercice de la section 7 -- remontees en fin de carnet.
- F7 : exercice exoLibre obsolete (remplace par Exercice 1 executable).

Normalisation nbformat : la cellule markdown « import-torchlean » portait
outputs/execution_count, ce qui rendait le carnet invalide au schema et
bloquait toute ecriture (motif mesure sur 3 des 92 carnets Lean).

Re-execution Papermill complete du carnet (13/13 cellules, 0 erreur,
execution_count contigus 1..13, ids de cellules preserves), sorties commitees.
Le kernel Lean tourne sur un lac minimal sans dependances : le carnet est
auto-contenu (aucun import en cellule de code).

See #17357

Co-Authored-By: Claude Haiku 4.5 (1M context) <noreply@anthropic.com>
---
 .../SymbolicAI/Lean/Lean-11-TorchLean.ipynb   | 2636 ++++++++---------
 1 file changed, 1298 insertions(+), 1338 deletions(-)

diff --git a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
index 0153fe445b..1fb85664a6 100644
--- a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
+++ b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
@@ -5,10 +5,10 @@
    "id": "title-cell",
    "metadata": {
     "papermill": {
-     "duration": 0.005161,
-     "end_time": "2026-06-18T03:11:10.105035+00:00",
+     "duration": 0.009171,
+     "end_time": "2026-10-09T15:38:30.204181+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:10.099874+00:00",
+     "start_time": "2026-10-09T15:38:30.195010+00:00",
      "status": "completed"
     },
     "tags": []
@@ -178,16 +178,16 @@
    "id": "verify-installation",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:10.116131Z",
-     "iopub.status.busy": "2026-06-18T03:11:10.115944Z",
-     "iopub.status.idle": "2026-06-18T03:11:11.358360Z",
-     "shell.execute_reply": "2026-06-18T03:11:11.357111Z"
+     "iopub.execute_input": "2026-10-09T15:38:30.246100Z",
+     "iopub.status.busy": "2026-10-09T15:38:30.245915Z",
+     "iopub.status.idle": "2026-10-09T15:38:33.029782Z",
+     "shell.execute_reply": "2026-10-09T15:38:33.028822Z"
     },
     "papermill": {
-     "duration": 1.248904,
-     "end_time": "2026-06-18T03:11:11.358883+00:00",
+     "duration": 2.803297,
+     "end_time": "2026-10-09T15:38:33.031102+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:10.109979+00:00",
+     "start_time": "2026-10-09T15:38:30.227805+00:00",
      "status": "completed"
     },
     "tags": []
@@ -206,17 +206,17 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verification de l&#39;environnement Lean pour TorchLean</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verification de l'environnement Lean pour TorchLean</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifier la version de Lean</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk0\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk0\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>Lean<span class=\"bp\">.</span>versionString</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;4.30.0&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk0\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk0\"><span class=\"k\">#eval</span><span class=\"w\"> </span>Lean.versionString</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"4.33.0\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifier que Lake est disponible</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Lake package manager required&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Lake package manager required&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Lake package manager required\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Lake package manager required\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Informations sur Mathlib</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk2\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk2\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Mathlib4 required for TorchLean proofs&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Mathlib4 required for TorchLean proofs&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk2\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk2\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Mathlib4 required for TorchLean proofs\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Mathlib4 required for TorchLean proofs\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 0</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -229,7 +229,7 @@
        " [{\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 6, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 6, \"column\": 5},\r\n",
-       "   \"data\": \"\\\"4.30.0\\\"\"},\r\n",
+       "   \"data\": \"\\\"4.33.0\\\"\"},\r\n",
        "  {\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 9, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 9, \"column\": 5},\r\n",
@@ -249,7 +249,7 @@
        "\n",
        "-- Verifier la version de Lean\n",
        "#eval Lean.versionString\n",
-       "─────▶  \"4.30.0\"\n",
+       "─────▶  \"4.33.0\"\n",
        "\n",
        "-- Verifier que Lake est disponible\n",
        "#eval \"Lake package manager required\"\n",
@@ -267,7 +267,7 @@
        " [{\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 6, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 6, \"column\": 5},\r\n",
-       "   \"data\": \"\\\"4.30.0\\\"\"},\r\n",
+       "   \"data\": \"\\\"4.33.0\\\"\"},\r\n",
        "  {\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 9, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 9, \"column\": 5},\r\n",
@@ -303,10 +303,10 @@
    "id": "interpretation-installation",
    "metadata": {
     "papermill": {
-     "duration": 0.005114,
-     "end_time": "2026-06-18T03:11:11.369610+00:00",
+     "duration": 0.019864,
+     "end_time": "2026-10-09T15:38:33.059470+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.364496+00:00",
+     "start_time": "2026-10-09T15:38:33.039606+00:00",
      "status": "completed"
     },
     "tags": []
@@ -328,10 +328,10 @@
    "id": "import-torchlean",
    "metadata": {
     "papermill": {
-     "duration": 0.004991,
-     "end_time": "2026-06-18T03:11:11.391263+00:00",
+     "duration": 0.01904,
+     "end_time": "2026-10-09T15:38:33.101177+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.386272+00:00",
+     "start_time": "2026-10-09T15:38:33.082137+00:00",
      "status": "completed"
     },
     "tags": []
@@ -367,10 +367,10 @@
    "id": "interpretation-imports",
    "metadata": {
     "papermill": {
-     "duration": 0.004682,
-     "end_time": "2026-06-18T03:11:11.401181+00:00",
+     "duration": 0.015962,
+     "end_time": "2026-10-09T15:38:33.135042+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.396499+00:00",
+     "start_time": "2026-10-09T15:38:33.119080+00:00",
      "status": "completed"
     },
     "tags": []
@@ -396,10 +396,10 @@
    "id": "separator-1",
    "metadata": {
     "papermill": {
-     "duration": 0.004348,
-     "end_time": "2026-06-18T03:11:11.409979+00:00",
+     "duration": 0.019076,
+     "end_time": "2026-10-09T15:38:33.168905+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.405631+00:00",
+     "start_time": "2026-10-09T15:38:33.149829+00:00",
      "status": "completed"
     },
     "tags": []
@@ -409,21 +409,7 @@
     "\n",
     "<a id=\"3-api\"></a>\n",
     "\n",
-    "## 3. API PyTorch-style en Lean\n",
-    "\n",
-    "### 3.1 Tenseurs : structure de base\n",
-    "\n",
-    "TorchLean définit les tenseurs comme des structures Lean avec :\n",
-    "- Dimensions (shape)\n",
-    "- Données Float32\n",
-    "- Méthodes de manipulation\n",
-    "\n",
-    "```lean\n",
-    "structure Tensor where\n",
-    "  shape : List Nat\n",
-    "  data : Array Float32\n",
-    "  deriving Repr\n",
-    "```"
+    "## 3. API PyTorch-style en Lean\n"
    ]
   },
   {
@@ -431,10 +417,10 @@
    "id": "hhzlw6jqlq8",
    "metadata": {
     "papermill": {
-     "duration": 0.004248,
-     "end_time": "2026-06-18T03:11:11.418612+00:00",
+     "duration": 0.01474,
+     "end_time": "2026-10-09T15:38:33.200509+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.414364+00:00",
+     "start_time": "2026-10-09T15:38:33.185769+00:00",
      "status": "completed"
     },
     "tags": []
@@ -484,9 +470,6 @@
     "\n",
     "***\n",
     "\n",
-    "<a id=\"3-api\"></a>\n",
-    "## 3. API PyTorch-style en Lean\n",
-    "\n",
     "### 3.1 Tenseurs : structure de base\n",
     "\n",
     "TorchLean définit les tenseurs comme des structures Lean avec :\n",
@@ -499,7 +482,7 @@
     "  shape : List Nat\n",
     "  data : Array Float32\n",
     "  deriving Repr\n",
-    "```"
+    "```\n"
    ]
   },
   {
@@ -508,16 +491,16 @@
    "id": "tensor-basics",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:11.428989Z",
-     "iopub.status.busy": "2026-06-18T03:11:11.428829Z",
-     "iopub.status.idle": "2026-06-18T03:11:11.584628Z",
-     "shell.execute_reply": "2026-06-18T03:11:11.583872Z"
+     "iopub.execute_input": "2026-10-09T15:38:33.238807Z",
+     "iopub.status.busy": "2026-10-09T15:38:33.238617Z",
+     "iopub.status.idle": "2026-10-09T15:38:33.465317Z",
+     "shell.execute_reply": "2026-10-09T15:38:33.463367Z"
     },
     "papermill": {
-     "duration": 0.162461,
-     "end_time": "2026-06-18T03:11:11.585367+00:00",
+     "duration": 0.248195,
+     "end_time": "2026-10-09T15:38:33.466582+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.422906+00:00",
+     "start_time": "2026-10-09T15:38:33.218387+00:00",
      "status": "completed"
     },
     "tags": []
@@ -539,27 +522,27 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 1 : Creation de tenseurs simples</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d&#39;un type de tenseur simplifie</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d'un type de tenseur simplifie</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (shape<span class=\"w\"> </span>:<span class=\"w\"> </span>List<span class=\"w\"> </span>Nat)</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (data<span class=\"w\"> </span>:<span class=\"w\"> </span>List<span class=\"w\"> </span>Float)<span class=\"w\">  </span><span class=\"c1\">-- Simplifie avec Float pour l&#39;exemple</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (data<span class=\"w\"> </span>:<span class=\"w\"> </span>List<span class=\"w\"> </span>Float)<span class=\"w\">  </span><span class=\"c1\">-- Simplifie avec Float pour l'exemple</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : tenseur scalaire</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>scalar<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">3.14</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>scalar<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">14</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : vecteur de taille 3</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>vector<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">1.0</span>,<span class=\"w\"> </span><span class=\"mf\">2.0</span>,<span class=\"w\"> </span><span class=\"mf\">3.0</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>vector<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">0</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : matrice 2x3</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>matrix<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">1.0</span>,<span class=\"w\"> </span><span class=\"mf\">2.0</span>,<span class=\"w\"> </span><span class=\"mf\">3.0</span>,<span class=\"w\"> </span><span class=\"mf\">4.0</span>,<span class=\"w\"> </span><span class=\"mf\">5.0</span>,<span class=\"w\"> </span><span class=\"mf\">6.0</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>matrix<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">4</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">5</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">6</span><span class=\"bp\">.</span><span class=\"mi\">0</span>]<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk3\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk3\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>scalar</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">3.140000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk4\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk4\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>vector</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">1.000000</span>,<span class=\"w\"> </span><span class=\"mf\">2.000000</span>,<span class=\"w\"> </span><span class=\"mf\">3.000000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk5\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk5\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>matrix</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">1.000000</span>,<span class=\"w\"> </span><span class=\"mf\">2.000000</span>,<span class=\"w\"> </span><span class=\"mf\">3.000000</span>,<span class=\"w\"> </span><span class=\"mf\">4.000000</span>,<span class=\"w\"> </span><span class=\"mf\">5.000000</span>,<span class=\"w\"> </span><span class=\"mf\">6.000000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk3\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk3\"><span class=\"k\">#eval</span><span class=\"w\"> </span>scalar</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">140000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk4\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk4\"><span class=\"k\">#eval</span><span class=\"w\"> </span>vector</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk5\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk5\"><span class=\"k\">#eval</span><span class=\"w\"> </span>matrix</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">3</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">4</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">5</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">6</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>]<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 1</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -674,10 +657,10 @@
    "id": "interpretation-tensor-basics",
    "metadata": {
     "papermill": {
-     "duration": 0.005062,
-     "end_time": "2026-06-18T03:11:11.595442+00:00",
+     "duration": 0.014454,
+     "end_time": "2026-10-09T15:38:33.489213+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.590380+00:00",
+     "start_time": "2026-10-09T15:38:33.474759+00:00",
      "status": "completed"
     },
     "tags": []
@@ -699,10 +682,10 @@
    "id": "layers-intro",
    "metadata": {
     "papermill": {
-     "duration": 0.005438,
-     "end_time": "2026-06-18T03:11:11.606316+00:00",
+     "duration": 0.016697,
+     "end_time": "2026-10-09T15:38:33.521652+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.600878+00:00",
+     "start_time": "2026-10-09T15:38:33.504955+00:00",
      "status": "completed"
     },
     "tags": []
@@ -724,16 +707,16 @@
    "id": "linear-layer",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:11.617439Z",
-     "iopub.status.busy": "2026-06-18T03:11:11.617268Z",
-     "iopub.status.idle": "2026-06-18T03:11:11.878541Z",
-     "shell.execute_reply": "2026-06-18T03:11:11.877860Z"
+     "iopub.execute_input": "2026-10-09T15:38:33.560170Z",
+     "iopub.status.busy": "2026-10-09T15:38:33.559974Z",
+     "iopub.status.idle": "2026-10-09T15:38:33.961018Z",
+     "shell.execute_reply": "2026-10-09T15:38:33.960147Z"
     },
     "papermill": {
-     "duration": 0.2736,
-     "end_time": "2026-06-18T03:11:11.884835+00:00",
+     "duration": 0.433671,
+     "end_time": "2026-10-09T15:38:33.974727+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.611235+00:00",
+     "start_time": "2026-10-09T15:38:33.541056+00:00",
      "status": "completed"
     },
     "tags": []
@@ -752,11 +735,11 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 2 : Definition d&#39;une couche Linear</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 2 : Definition d'une couche Linear</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d&#39;une couche Linear simplifiee</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>LinearLayer<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d'une couche Linear simplifiee</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>LinearLayer<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (inFeatures<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (outFeatures<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (weight<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor)<span class=\"w\">  </span><span class=\"c1\">-- shape: [outFeatures, inFeatures]</span></span></span></pre>\n",
@@ -764,900 +747,903 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Fonction de forward pass</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk6\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk6\"><span class=\"kn\">def</span><span class=\"w\"> </span>linearForward<span class=\"w\"> </span>(layer<span class=\"w\"> </span>:<span class=\"w\"> </span>LinearLayer)<span class=\"w\"> </span>(input<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor)<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"><span class=\"bp\">🟨</span><span class=\"w\"> </span>unused<span class=\"w\"> </span><span class=\"kn\">variable</span><span class=\"w\"> </span><span class=\"ss\">`input</span><span class=\"bp\">`</span>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk6\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk6\"><span class=\"kd\">def</span><span class=\"w\"> </span>linearForward<span class=\"w\"> </span>(layer<span class=\"w\"> </span>:<span class=\"w\"> </span>LinearLayer)<span class=\"w\"> </span>(input<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor)<span class=\"w\"> </span>:<span class=\"w\"> </span>SimpleTensor<span class=\"w\"> </span>:=</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"><span class=\"bp\">🟨</span><span class=\"w\"> </span>Variable<span class=\"w\"> </span>name<span class=\"w\"> </span><span class=\"ss\">`input</span><span class=\"bp\">`</span><span class=\"w\"> </span>is<span class=\"w\"> </span>not<span class=\"w\"> </span>explicitly<span class=\"w\"> </span>referenced<span class=\"bp\">.</span>\n",
+       "\n",
+       "Hint:<span class=\"w\"> </span>The<span class=\"w\"> </span>binding<span class=\"w\"> </span>can<span class=\"w\"> </span>be<span class=\"w\"> </span>removed<span class=\"w\"> </span>(<span class=\"k\">if</span><span class=\"w\"> </span>unused)<span class=\"w\"> </span>or<span class=\"w\"> </span>named<span class=\"w\"> </span><span class=\"ss\">`_</span><span class=\"bp\">`</span><span class=\"w\"> </span>(<span class=\"k\">if</span><span class=\"w\"> </span>used<span class=\"w\"> </span>implicitly)<span class=\"bp\">.</span><span class=\"w\"> </span>Alternatively,<span class=\"w\"> </span><span class=\"kd\">prefix</span><span class=\"w\"> </span>the<span class=\"w\"> </span>name<span class=\"w\"> </span><span class=\"k\">with</span><span class=\"w\"> </span><span class=\"ss\">`_</span><span class=\"bp\">`</span><span class=\"w\"> </span>to<span class=\"w\"> </span>silence<span class=\"w\"> </span>this<span class=\"w\"> </span>warning:\n",
+       "<span class=\"w\">  </span>[apply]<span class=\"w\"> </span>_input\n",
        "\n",
-       "Note:<span class=\"w\"> </span>This<span class=\"w\"> </span>linter<span class=\"w\"> </span>can<span class=\"w\"> </span>be<span class=\"w\"> </span>disabled<span class=\"w\"> </span><span class=\"k\">with</span><span class=\"w\"> </span><span class=\"ss\">`set_option</span><span class=\"w\"> </span>linter<span class=\"bp\">.</span>unusedVariables<span class=\"w\"> </span>false<span class=\"bp\">`</span></blockquote></div></div></small></span></pre>\n",
+       "Note:<span class=\"w\"> </span>This<span class=\"w\"> </span>linter<span class=\"w\"> </span>can<span class=\"w\"> </span>be<span class=\"w\"> </span>disabled<span class=\"w\"> </span><span class=\"k\">with</span><span class=\"w\"> </span><span class=\"ss\">`set_option</span><span class=\"w\"> </span>linter.unusedVariables<span class=\"w\"> </span>false<span class=\"bp\">`</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"c1\">-- Implementation simplifiee (pas la vraie multiplication matricielle)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[layer<span class=\"bp\">.</span>outFeatures]</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List<span class=\"bp\">.</span>replicate<span class=\"w\"> </span>layer<span class=\"bp\">.</span>outFeatures<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\">  </span><span class=\"c1\">-- Placeholder</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[layer.outFeatures]</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List.replicate<span class=\"w\"> </span>layer.outFeatures<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\">  </span><span class=\"c1\">-- Placeholder</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : couche 784 -&gt; 10 (comme pour MNIST)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>mnistLayer<span class=\"w\"> </span>:<span class=\"w\"> </span>LinearLayer<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>mnistLayer<span class=\"w\"> </span>:<span class=\"w\"> </span>LinearLayer<span class=\"w\"> </span>:=</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>inFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">784</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    outFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">10</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    weight<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>,<span class=\"w\"> </span><span class=\"mi\">784</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List<span class=\"bp\">.</span>replicate<span class=\"w\"> </span>(<span class=\"mi\">10</span><span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span><span class=\"mi\">784</span>)<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\"> </span>}</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    bias<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List<span class=\"bp\">.</span>replicate<span class=\"w\"> </span><span class=\"mi\">10</span><span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    weight<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>,<span class=\"w\"> </span><span class=\"mi\">784</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List.replicate<span class=\"w\"> </span>(<span class=\"mi\">10</span><span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span><span class=\"mi\">784</span>)<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    bias<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>List.replicate<span class=\"w\"> </span><span class=\"mi\">10</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk7\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk7\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>mnistLayer</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>inFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">784</span>,\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk7\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk7\"><span class=\"k\">#eval</span><span class=\"w\"> </span>mnistLayer</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>inFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">784</span>,\n",
        "<span class=\"w\">  </span>outFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">10</span>,\n",
        "<span class=\"w\">  </span>weight<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>,<span class=\"w\"> </span><span class=\"mi\">784</span>],\n",
-       "<span class=\"w\">              </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
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-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
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-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                       </span><span class=\"mf\">0.000000</span>]<span class=\"w\"> </span>},\n",
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+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
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+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                       </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>]<span class=\"w\"> </span>},\n",
        "<span class=\"w\">  </span>bias<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>],\n",
-       "<span class=\"w\">            </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,\n",
-       "<span class=\"w\">                     </span><span class=\"mf\">0.000000</span>]<span class=\"w\"> </span>}<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<span class=\"w\">            </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,\n",
+       "<span class=\"w\">                     </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>]<span class=\"w\"> </span>}<span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 2</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -1671,7 +1657,7 @@
        "   \"pos\": {\"line\": 14, \"column\": 41},\r\n",
        "   \"endPos\": {\"line\": 14, \"column\": 46},\r\n",
        "   \"data\":\r\n",
-       "   \"unused variable `input`\\n\\nNote: This linter can be disabled with `set_option linter.unusedVariables false`\"},\r\n",
+       "   \"Variable name `input` is not explicitly referenced.\\n\\nHint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:\\n  [apply] _input\\n\\nNote: This linter can be disabled with `set_option linter.unusedVariables false`\"},\r\n",
        "  {\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 28, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 28, \"column\": 5},\r\n",
@@ -1696,7 +1682,10 @@
        "\n",
        "-- Fonction de forward pass\n",
        "def linearForward (layer : LinearLayer) (input : SimpleTensor) : SimpleTensor :=\n",
-       "                                         ─────▶ 🟨 unused variable `input`\n",
+       "                                         ─────▶ 🟨 Variable name `input` is not explicitly referenced.\n",
+       "\n",
+       "Hint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:\n",
+       "  [apply] _input\n",
        "\n",
        "Note: This linter can be disabled with `set_option linter.unusedVariables false`\n",
        "  -- Implementation simplifiee (pas la vraie multiplication matricielle)\n",
@@ -2601,7 +2590,7 @@
        "   \"pos\": {\"line\": 14, \"column\": 41},\r\n",
        "   \"endPos\": {\"line\": 14, \"column\": 46},\r\n",
        "   \"data\":\r\n",
-       "   \"unused variable `input`\\n\\nNote: This linter can be disabled with `set_option linter.unusedVariables false`\"},\r\n",
+       "   \"Variable name `input` is not explicitly referenced.\\n\\nHint: The binding can be removed (if unused) or named `_` (if used implicitly). Alternatively, prefix the name with `_` to silence this warning:\\n  [apply] _input\\n\\nNote: This linter can be disabled with `set_option linter.unusedVariables false`\"},\r\n",
        "  {\"severity\": \"info\",\r\n",
        "   \"pos\": {\"line\": 28, \"column\": 0},\r\n",
        "   \"endPos\": {\"line\": 28, \"column\": 5},\r\n",
@@ -2650,10 +2639,10 @@
    "id": "interpretation-linear-layer",
    "metadata": {
     "papermill": {
-     "duration": 0.010647,
-     "end_time": "2026-06-18T03:11:11.905672+00:00",
+     "duration": 0.032102,
+     "end_time": "2026-10-09T15:38:34.031153+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.895025+00:00",
+     "start_time": "2026-10-09T15:38:33.999051+00:00",
      "status": "completed"
     },
     "tags": []
@@ -2678,10 +2667,10 @@
    "id": "sequential-intro",
    "metadata": {
     "papermill": {
-     "duration": 0.010607,
-     "end_time": "2026-06-18T03:11:11.930477+00:00",
+     "duration": 0.032927,
+     "end_time": "2026-10-09T15:38:34.100722+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.919870+00:00",
+     "start_time": "2026-10-09T15:38:34.067795+00:00",
      "status": "completed"
     },
     "tags": []
@@ -2707,16 +2696,16 @@
    "id": "sequential-model",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:11.952539Z",
-     "iopub.status.busy": "2026-06-18T03:11:11.952367Z",
-     "iopub.status.idle": "2026-06-18T03:11:12.109778Z",
-     "shell.execute_reply": "2026-06-18T03:11:12.108811Z"
+     "iopub.execute_input": "2026-10-09T15:38:34.161918Z",
+     "iopub.status.busy": "2026-10-09T15:38:34.161562Z",
+     "iopub.status.idle": "2026-10-09T15:38:34.377581Z",
+     "shell.execute_reply": "2026-10-09T15:38:34.376364Z"
     },
     "papermill": {
-     "duration": 0.168922,
-     "end_time": "2026-06-18T03:11:12.110708+00:00",
+     "duration": 0.245919,
+     "end_time": "2026-10-09T15:38:34.378464+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:11.941786+00:00",
+     "start_time": "2026-10-09T15:38:34.132545+00:00",
      "status": "completed"
     },
     "tags": []
@@ -2740,27 +2729,27 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Type pour representer un module</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Note : `deriving Repr` est necessaire pour reutiliser `Module` dans</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- d&#39;autres structures derivant `Repr` (ex. `ExportableModel` plus loin).</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Lean genere automatiquement l&#39;instance recursive `Repr Module` ET</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- d'autres structures derivant `Repr` (ex. `ExportableModel` plus loin).</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Lean genere automatiquement l'instance recursive `Repr Module` ET</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- `Repr (List Module)` grace au cas `sequential`.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">inductive</span><span class=\"w\"> </span>Module<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">inductive</span><span class=\"w\"> </span>Module<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>linear<span class=\"w\"> </span>:<span class=\"w\"> </span>LinearLayer<span class=\"w\"> </span><span class=\"bp\">→</span><span class=\"w\"> </span>Module</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>relu<span class=\"w\"> </span>:<span class=\"w\"> </span>Module</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>sequential<span class=\"w\"> </span>:<span class=\"w\"> </span>List<span class=\"w\"> </span>Module<span class=\"w\"> </span><span class=\"bp\">→</span><span class=\"w\"> </span>Module</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : Mini-MLP 784 -&gt; 128 -&gt; 10</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>miniMLP<span class=\"w\"> </span>:<span class=\"w\"> </span>Module<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Module<span class=\"bp\">.</span>sequential<span class=\"w\"> </span>[</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module<span class=\"bp\">.</span>linear<span class=\"w\"> </span>(</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>miniMLP<span class=\"w\"> </span>:<span class=\"w\"> </span>Module<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Module.sequential<span class=\"w\"> </span>[</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module.linear<span class=\"w\"> </span>(</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">      {<span class=\"w\"> </span>inFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">784</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">        outFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">128</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">        weight<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">128</span>,<span class=\"w\"> </span><span class=\"mi\">784</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[]<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">        bias<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">128</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[]<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">      }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    ),</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module<span class=\"bp\">.</span>relu,</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module<span class=\"bp\">.</span>linear<span class=\"w\"> </span>(</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module.relu,</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    Module.linear<span class=\"w\"> </span>(</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">      {<span class=\"w\"> </span>inFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">128</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">        outFeatures<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">10</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">        weight<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>shape<span class=\"w\"> </span>:=<span class=\"w\"> </span>[<span class=\"mi\">10</span>,<span class=\"w\"> </span><span class=\"mi\">128</span>],<span class=\"w\"> </span>data<span class=\"w\"> </span>:=<span class=\"w\"> </span>[]<span class=\"w\"> </span>}</span></span></pre>\n",
@@ -2769,7 +2758,7 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    )</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  ]</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk8\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk8\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Mini-MLP defined with 3 layers&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Mini-MLP defined with 3 layers&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk8\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk8\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Mini-MLP defined with 3 layers\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Mini-MLP defined with 3 layers\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 3</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -2886,10 +2875,10 @@
    "id": "interpretation-sequential",
    "metadata": {
     "papermill": {
-     "duration": 0.010003,
-     "end_time": "2026-06-18T03:11:12.130406+00:00",
+     "duration": 0.028525,
+     "end_time": "2026-10-09T15:38:34.431025+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.120403+00:00",
+     "start_time": "2026-10-09T15:38:34.402500+00:00",
      "status": "completed"
     },
     "tags": []
@@ -2923,10 +2912,10 @@
    "id": "separator-2",
    "metadata": {
     "papermill": {
-     "duration": 0.010312,
-     "end_time": "2026-06-18T03:11:12.150108+00:00",
+     "duration": 0.025948,
+     "end_time": "2026-10-09T15:38:34.484692+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.139796+00:00",
+     "start_time": "2026-10-09T15:38:34.458744+00:00",
      "status": "completed"
     },
     "tags": []
@@ -2977,16 +2966,16 @@
    "id": "rounding-modes",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-08-15T23:17:26.559766Z",
-     "iopub.status.busy": "2026-08-15T23:17:26.559507Z",
-     "iopub.status.idle": "2026-08-15T23:17:26.782645Z",
-     "shell.execute_reply": "2026-08-15T23:17:26.781375Z"
+     "iopub.execute_input": "2026-10-09T15:38:34.547169Z",
+     "iopub.status.busy": "2026-10-09T15:38:34.546849Z",
+     "iopub.status.idle": "2026-10-09T15:38:34.865428Z",
+     "shell.execute_reply": "2026-10-09T15:38:34.864215Z"
     },
     "papermill": {
-     "duration": 0.249102,
-     "end_time": "2026-08-15T23:17:26.411099",
+     "duration": 0.352697,
+     "end_time": "2026-10-09T15:38:34.866774+00:00",
      "exception": false,
-     "start_time": "2026-08-15T23:17:26.161997",
+     "start_time": "2026-10-09T15:38:34.514077+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3005,11 +2994,11 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 4 : Modes d&#39;arrondi IEEE-754</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 4 : Modes d'arrondi IEEE-754</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition du mode d&#39;arrondi</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">inductive</span><span class=\"w\"> </span>RoundingMode<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition du mode d'arrondi</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">inductive</span><span class=\"w\"> </span>RoundingMode<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>RNE<span class=\"w\">  </span><span class=\"c1\">-- Round to Nearest, ties to Even (defaut)</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>RNA<span class=\"w\">  </span><span class=\"c1\">-- Round to Nearest, ties Away from zero</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span>RTP<span class=\"w\">  </span><span class=\"c1\">-- Round Toward Positive (ceil)</span></span></span></pre>\n",
@@ -3019,38 +3008,38 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Helper : troncature vers zero (equivalent IEEE-754 RTZ)</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- floor pour les positifs, ceil pour les negatifs.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>floatTrunc<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>floor<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>ceil<span class=\"w\"> </span>x</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>floatTrunc<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>Float.floor<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span>Float.ceil<span class=\"w\"> </span>x</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- RNE (Round to Nearest, ties to Even) : sur un tie (fraction = 0.5),</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- on arrondit vers l&#39;entier pair le plus proche.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>isEvenInt<span class=\"w\"> </span>(n<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=<span class=\"w\"> </span>Float<span class=\"bp\">.</span>beq<span class=\"w\"> </span>(Float<span class=\"bp\">.</span>floor<span class=\"w\"> </span>(n<span class=\"w\"> </span><span class=\"bp\">/</span><span class=\"w\"> </span><span class=\"mi\">2</span>)<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span><span class=\"mi\">2</span>)<span class=\"w\"> </span>n</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- on arrondit vers l'entier pair le plus proche.</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>isEvenInt<span class=\"w\"> </span>(n<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=<span class=\"w\"> </span>Float.beq<span class=\"w\"> </span>(Float.floor<span class=\"w\"> </span>(n<span class=\"w\"> </span><span class=\"bp\">/</span><span class=\"w\"> </span><span class=\"mi\">2</span>)<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span><span class=\"mi\">2</span>)<span class=\"w\"> </span>n</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>roundRnePos<span class=\"w\"> </span>(y<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">let</span><span class=\"w\"> </span>n<span class=\"w\"> </span>:=<span class=\"w\"> </span>Float<span class=\"bp\">.</span>floor<span class=\"w\"> </span>y</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>roundRnePos<span class=\"w\"> </span>(y<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">let</span><span class=\"w\"> </span>n<span class=\"w\"> </span>:=<span class=\"w\"> </span>Float.floor<span class=\"w\"> </span>y</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">let</span><span class=\"w\"> </span>d<span class=\"w\"> </span>:=<span class=\"w\"> </span>y<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"w\"> </span>n</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>d<span class=\"w\"> </span><span class=\"bp\">&lt;</span><span class=\"w\"> </span><span class=\"mf\">0.5</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>n</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>d<span class=\"w\"> </span><span class=\"bp\">&gt;</span><span class=\"w\"> </span><span class=\"mf\">0.5</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>n<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>d<span class=\"w\"> </span><span class=\"bp\">&lt;</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>n</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>d<span class=\"w\"> </span><span class=\"bp\">&gt;</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>n<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>isEvenInt<span class=\"w\"> </span>n<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>n<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span>n<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>roundRne<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>roundRnePos<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span><span class=\"bp\">-</span>roundRnePos<span class=\"w\"> </span>(<span class=\"bp\">-</span>x)</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>roundRne<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>roundRnePos<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span><span class=\"bp\">-</span>roundRnePos<span class=\"w\"> </span>(<span class=\"bp\">-</span>x)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">match</span><span class=\"w\"> </span>mode<span class=\"w\"> </span><span class=\"k\">with</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>roundRne<span class=\"w\"> </span>x</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RNA<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>floor<span class=\"w\"> </span>(x<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mf\">0.5</span>)<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>ceil<span class=\"w\"> </span>(x<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"w\"> </span><span class=\"mf\">0.5</span>)</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RTP<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>ceil<span class=\"w\"> </span>x</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RTN<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>Float<span class=\"bp\">.</span>floor<span class=\"w\"> </span>x</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RNA<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>Float.floor<span class=\"w\"> </span>(x<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span>Float.ceil<span class=\"w\"> </span>(x<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RTP<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>Float.ceil<span class=\"w\"> </span>x</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RTN<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>Float.floor<span class=\"w\"> </span>x</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">|</span><span class=\"w\"> </span><span class=\"bp\">.</span>RTZ<span class=\"w\"> </span><span class=\"bp\">=&gt;</span><span class=\"w\"> </span>floatTrunc<span class=\"w\"> </span>x</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Demonstration</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk9\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk9\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mf\">1.5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">2.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chka\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chka\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mf\">2.5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">2.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkb\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkb\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>(<span class=\"bp\">-</span><span class=\"mf\">1.5</span>)<span class=\"w\"> </span><span class=\"c1\">-- -2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"bp\">-</span><span class=\"mf\">2.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkc\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkc\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTZ<span class=\"w\"> </span><span class=\"mf\">1.5</span><span class=\"w\">    </span><span class=\"c1\">-- 1.0 (truncate)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">1.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkd\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkd\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTP<span class=\"w\"> </span><span class=\"mf\">1.5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (ceil)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">2.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chke\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chke\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTN<span class=\"w\"> </span><span class=\"mf\">1.5</span><span class=\"w\">    </span><span class=\"c1\">-- 1.0 (floor)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">1.000000</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkf\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkf\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNA<span class=\"w\"> </span><span class=\"mf\">2.5</span><span class=\"w\">    </span><span class=\"c1\">-- 3.0 (ties away from zero)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">3.000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk9\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk9\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chka\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chka\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkb\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkb\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>(<span class=\"bp\">-</span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)<span class=\"w\"> </span><span class=\"c1\">-- -2.0 (nearest even)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"bp\">-</span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkc\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkc\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTZ<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 1.0 (truncate)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkd\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkd\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTP<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 2.0 (ceil)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chke\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chke\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTN<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 1.0 (floor)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkf\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkf\"><span class=\"k\">#eval</span><span class=\"w\"> </span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNA<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">    </span><span class=\"c1\">-- 3.0 (ties away from zero)</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 4</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -3243,10 +3232,10 @@
    "id": "interpretation-rounding",
    "metadata": {
     "papermill": {
-     "duration": 0.010039,
-     "end_time": "2026-06-18T03:11:12.347558+00:00",
+     "duration": 0.030415,
+     "end_time": "2026-10-09T15:38:34.922366+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.337519+00:00",
+     "start_time": "2026-10-09T15:38:34.891951+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3275,16 +3264,16 @@
    "id": "float32-properties",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:12.368509Z",
-     "iopub.status.busy": "2026-06-18T03:11:12.368342Z",
-     "iopub.status.idle": "2026-06-18T03:11:12.524281Z",
-     "shell.execute_reply": "2026-06-18T03:11:12.523386Z"
+     "iopub.execute_input": "2026-10-09T15:38:34.975747Z",
+     "iopub.status.busy": "2026-10-09T15:38:34.975467Z",
+     "iopub.status.idle": "2026-10-09T15:38:35.199130Z",
+     "shell.execute_reply": "2026-10-09T15:38:35.197449Z"
     },
     "papermill": {
-     "duration": 0.167825,
-     "end_time": "2026-06-18T03:11:12.524882+00:00",
+     "duration": 0.252414,
+     "end_time": "2026-10-09T15:38:35.200264+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.357057+00:00",
+     "start_time": "2026-10-09T15:38:34.947850+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3303,42 +3292,42 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 5 : Proprietes formelles de l&#39;arrondi</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 5 : Proprietes formelles de l'arrondi</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Note pedagogique : `Float` en Lean est un type opaque enveloppant</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- IEEE-754. Son egalite n&#39;est pas `Decidable`, donc on illustre les</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- IEEE-754. Son egalite n'est pas `Decidable`, donc on illustre les</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- proprietes par des fonctions booleennes verifiees par `#eval`</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- (l&#39;equivalent Lean d&#39;un property-based test pour le kernel Jupyter).</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- (l'equivalent Lean d'un property-based test pour le kernel Jupyter).</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Une vraie preuve universelle necessiterait TorchLean.Forum.Float32.</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Helper : valeur absolue Float</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>floatAbs<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span><span class=\"bp\">-</span>x</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>floatAbs<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"k\">else</span><span class=\"w\"> </span><span class=\"bp\">-</span>x</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- P1 : RTZ preserve le signe (test booleen)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>checkRtzNonNeg<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTZ<span class=\"w\"> </span>x)<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>checkRtzNonNeg<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RTZ<span class=\"w\"> </span>x)<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- P2 : RNE est symetrique (test booleen via Float.beq)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>checkRneSymmetric<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Float<span class=\"bp\">.</span>beq<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>(<span class=\"bp\">-</span>x))<span class=\"w\"> </span>(<span class=\"bp\">-</span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>x)</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>checkRneSymmetric<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Float.beq<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>(<span class=\"bp\">-</span>x))<span class=\"w\"> </span>(<span class=\"bp\">-</span>roundExample<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span>x)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- P3 : borne d&#39;erreur d&#39;arrondi (test booleen)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>checkErrorBounded<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  floatAbs<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span>mode<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"w\"> </span>x)<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span><span class=\"mf\">0.5</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- P3 : borne d'erreur d'arrondi (test booleen)</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>checkErrorBounded<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(x<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  floatAbs<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span>mode<span class=\"w\"> </span>x<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"w\"> </span>x)<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- P4 : invariance sur les entiers (test booleen)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>checkIntegerInvariance<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(n<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Float<span class=\"bp\">.</span>beq<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span>mode<span class=\"w\"> </span>n)<span class=\"w\"> </span>n</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>checkIntegerInvariance<span class=\"w\"> </span>(mode<span class=\"w\"> </span>:<span class=\"w\"> </span>RoundingMode)<span class=\"w\"> </span>(n<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Bool<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  Float.beq<span class=\"w\"> </span>(roundExample<span class=\"w\"> </span>mode<span class=\"w\"> </span>n)<span class=\"w\"> </span>n</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Petit theoreme sur Bool prouvable par decide (sanity check)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">example</span><span class=\"w\"> </span>:<span class=\"w\"> </span>(true<span class=\"w\"> </span><span class=\"bp\">&amp;&amp;</span><span class=\"w\"> </span>true)<span class=\"w\"> </span><span class=\"bp\">=</span><span class=\"w\"> </span>true<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"k\">by</span><span class=\"w\"> </span>decide</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">example</span><span class=\"w\"> </span>:<span class=\"w\"> </span>(true<span class=\"w\"> </span><span class=\"bp\">&amp;&amp;</span><span class=\"w\"> </span>true)<span class=\"w\"> </span><span class=\"bp\">=</span><span class=\"w\"> </span>true<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"kd\">by</span><span class=\"w\"> </span>decide</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifications concretes (kernel evaluation)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chke\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chke\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>(<span class=\"s2\">&quot;P1 RTZ(1.5) &gt;= 0   : &quot;</span>,<span class=\"w\"> </span>checkRtzNonNeg<span class=\"w\"> </span><span class=\"mf\">1.5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">&quot;P1 RTZ(1.5) &gt;= 0   : &quot;</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chkf\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chkf\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>(<span class=\"s2\">&quot;P2 RNE symmetric   : &quot;</span>,<span class=\"w\"> </span>checkRneSymmetric<span class=\"w\"> </span><span class=\"mf\">1.5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">&quot;P2 RNE symmetric   : &quot;</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk10\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk10\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>(<span class=\"s2\">&quot;P3 |RNE(1.5)-1.5| &lt;= 0.5 : &quot;</span>,<span class=\"w\"> </span>checkErrorBounded<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mf\">1.5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">&quot;P3 |RNE(1.5)-1.5| &lt;= 0.5 : &quot;</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk11\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk11\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>(<span class=\"s2\">&quot;P4 RNE(3.0) = 3.0  : &quot;</span>,<span class=\"w\"> </span>checkIntegerInvariance<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mf\">3.0</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">&quot;P4 RNE(3.0) = 3.0  : &quot;</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk12\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk12\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Proprietes Float32 verifiees ponctuellement (kernel evaluation)&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Proprietes Float32 verifiees ponctuellement (kernel evaluation)&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk10\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk10\"><span class=\"k\">#eval</span><span class=\"w\"> </span>(<span class=\"s2\">\"P1 RTZ(1.5) &gt;= 0   : \"</span>,<span class=\"w\"> </span>checkRtzNonNeg<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">\"P1 RTZ(1.5) &gt;= 0   : \"</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk11\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk11\"><span class=\"k\">#eval</span><span class=\"w\"> </span>(<span class=\"s2\">\"P2 RNE symmetric   : \"</span>,<span class=\"w\"> </span>checkRneSymmetric<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">\"P2 RNE symmetric   : \"</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk12\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk12\"><span class=\"k\">#eval</span><span class=\"w\"> </span>(<span class=\"s2\">\"P3 |RNE(1.5)-1.5| &lt;= 0.5 : \"</span>,<span class=\"w\"> </span>checkErrorBounded<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">5</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">\"P3 |RNE(1.5)-1.5| &lt;= 0.5 : \"</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk13\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk13\"><span class=\"k\">#eval</span><span class=\"w\"> </span>(<span class=\"s2\">\"P4 RNE(3.0) = 3.0  : \"</span>,<span class=\"w\"> </span>checkIntegerInvariance<span class=\"w\"> </span><span class=\"bp\">.</span>RNE<span class=\"w\"> </span><span class=\"mi\">3</span><span class=\"bp\">.</span><span class=\"mi\">0</span>)</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> (<span class=\"s2\">\"P4 RNE(3.0) = 3.0  : \"</span>,<span class=\"w\"> </span>true)</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk14\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk14\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Proprietes Float32 verifiees ponctuellement (kernel evaluation)\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Proprietes Float32 verifiees ponctuellement (kernel evaluation)\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 5</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -3495,10 +3484,10 @@
    "id": "interpretation-float32-theorems",
    "metadata": {
     "papermill": {
-     "duration": 0.010017,
-     "end_time": "2026-06-18T03:11:12.545478+00:00",
+     "duration": 0.026965,
+     "end_time": "2026-10-09T15:38:35.253868+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.535461+00:00",
+     "start_time": "2026-10-09T15:38:35.226903+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3525,10 +3514,10 @@
    "id": "lromuz607km",
    "metadata": {
     "papermill": {
-     "duration": 0.009957,
-     "end_time": "2026-06-18T03:11:12.565725+00:00",
+     "duration": 0.025563,
+     "end_time": "2026-10-09T15:38:35.308761+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.555768+00:00",
+     "start_time": "2026-10-09T15:38:35.283198+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3612,10 +3601,10 @@
    "id": "separator-3",
    "metadata": {
     "papermill": {
-     "duration": 0.010874,
-     "end_time": "2026-06-18T03:11:12.587115+00:00",
+     "duration": 0.027858,
+     "end_time": "2026-10-09T15:38:35.364482+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.576241+00:00",
+     "start_time": "2026-10-09T15:38:35.336624+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3658,9 +3647,7 @@
     "\n",
     "**LiRPA** (Lipschitz Regularized Provable Adversarial) :\n",
     "- Extension de CROWN\n",
-    "- Supporte plus d'activations\n",
-    "\n",
-    "### 5.4 Implémentation IBP dans TorchLean"
+    "- Supporte plus d'activations\n"
    ]
   },
   {
@@ -3668,10 +3655,10 @@
    "id": "pucaro04x5",
    "metadata": {
     "papermill": {
-     "duration": 0.011005,
-     "end_time": "2026-06-18T03:11:12.609224+00:00",
+     "duration": 0.033035,
+     "end_time": "2026-10-09T15:38:35.426064+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.598219+00:00",
+     "start_time": "2026-10-09T15:38:35.393029+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3753,9 +3740,7 @@
     "- Mais il peut aussi contenir des sorties **impossibles**\n",
     "- Le compromis : sécurité (garantie) vs précision (bornes serrées)\n",
     "\n",
-    "> **Note pédagogique** : Cette visualisation montre pourquoi IBP est rapide (calcul direct d'intervalles) mais peut produire des bornes trop lâches pour des réseaux profonds. C'est là que des méthodes comme CROWN deviennent nécessaires pour obtenir des bornes plus serrées.\n",
-    "\n",
-    "### 5.5 Implémentation IBP dans TorchLean"
+    "> **Note pédagogique** : Cette visualisation montre pourquoi IBP est rapide (calcul direct d'intervalles) mais peut produire des bornes trop lâches pour des réseaux profonds. C'est là que des méthodes comme CROWN deviennent nécessaires pour obtenir des bornes plus serrées.\n"
    ]
   },
   {
@@ -3764,16 +3749,16 @@
    "id": "ibp-implementation",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:12.630680Z",
-     "iopub.status.busy": "2026-06-18T03:11:12.630504Z",
-     "iopub.status.idle": "2026-06-18T03:11:12.766489Z",
-     "shell.execute_reply": "2026-06-18T03:11:12.765559Z"
+     "iopub.execute_input": "2026-10-09T15:38:35.492760Z",
+     "iopub.status.busy": "2026-10-09T15:38:35.492549Z",
+     "iopub.status.idle": "2026-10-09T15:38:35.721540Z",
+     "shell.execute_reply": "2026-10-09T15:38:35.720136Z"
     },
     "papermill": {
-     "duration": 0.147653,
-     "end_time": "2026-06-18T03:11:12.767113+00:00",
+     "duration": 0.263529,
+     "end_time": "2026-10-09T15:38:35.722665+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.619460+00:00",
+     "start_time": "2026-10-09T15:38:35.459136+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3795,31 +3780,31 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple 6 : Interval Bound Propagation (IBP)</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d&#39;un intervalle</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>Interval<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Definition d'un intervalle</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>Interval<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (lower<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (upper<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifier qu&#39;un intervalle est valide</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>Interval<span class=\"bp\">.</span>isValid<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>:<span class=\"w\"> </span><span class=\"kt\">Prop</span><span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  i<span class=\"bp\">.</span>lower<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span>i<span class=\"bp\">.</span>upper</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifier qu'un intervalle est valide</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>Interval.isValid<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>:<span class=\"w\"> </span><span class=\"kt\">Prop</span><span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  i.lower<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span>i.upper</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Propagation d&#39;intervalle pour ReLU</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"bp\">.</span>upper<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Propagation d'intervalle pour ReLU</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i.upper<span class=\"w\"> </span><span class=\"bp\">≤</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- Tout negatif</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"bp\">.</span>lower<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>lower,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>upper<span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- Tout positif</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>i.lower<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.lower,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.upper<span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- Tout positif</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>upper<span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- Traverse 0</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.upper<span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- Traverse 0</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : propagation sur un neurone</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>preActivation<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mf\">1.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.0</span><span class=\"w\"> </span>}</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>postActivation<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>preActivation</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>preActivation<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>postActivation<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>preActivation</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk13\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk13\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>preActivation<span class=\"w\">   </span><span class=\"c1\">-- [-1.0, 2.0]</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mf\">1.000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk14\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk14\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>postActivation<span class=\"w\">  </span><span class=\"c1\">-- [0.0, 2.0]</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk15\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk15\"><span class=\"k\">#eval</span><span class=\"w\"> </span>preActivation<span class=\"w\">   </span><span class=\"c1\">-- [-1.0, 2.0]</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk16\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk16\"><span class=\"k\">#eval</span><span class=\"w\"> </span>postActivation<span class=\"w\">  </span><span class=\"c1\">-- [0.0, 2.0]</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 6</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -3931,10 +3916,10 @@
    "id": "interpretation-ibp",
    "metadata": {
     "papermill": {
-     "duration": 0.010148,
-     "end_time": "2026-06-18T03:11:12.788117+00:00",
+     "duration": 0.036526,
+     "end_time": "2026-10-09T15:38:35.788130+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.777969+00:00",
+     "start_time": "2026-10-09T15:38:35.751604+00:00",
      "status": "completed"
     },
     "tags": []
@@ -3968,16 +3953,16 @@
    "id": "robustness-certificate",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:12.810559Z",
-     "iopub.status.busy": "2026-06-18T03:11:12.810396Z",
-     "iopub.status.idle": "2026-06-18T03:11:12.960139Z",
-     "shell.execute_reply": "2026-06-18T03:11:12.959280Z"
+     "iopub.execute_input": "2026-10-09T15:38:35.857801Z",
+     "iopub.status.busy": "2026-10-09T15:38:35.857513Z",
+     "iopub.status.idle": "2026-10-09T15:38:36.080089Z",
+     "shell.execute_reply": "2026-10-09T15:38:36.079151Z"
     },
     "papermill": {
-     "duration": 0.162341,
-     "end_time": "2026-06-18T03:11:12.960693+00:00",
+     "duration": 0.256753,
+     "end_time": "2026-10-09T15:38:36.081070+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.798352+00:00",
+     "start_time": "2026-10-09T15:38:35.824317+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4000,7 +3985,7 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Type de certificat</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>RobustnessCertificate<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>RobustnessCertificate<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (inputCenter<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\">  </span><span class=\"c1\">-- Entrée originale</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (epsilon<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\">      </span><span class=\"c1\">-- Rayon de la boule</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (predictedClass<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span><span class=\"c1\">-- Classe prédite</span></span></span></pre>\n",
@@ -4008,21 +3993,21 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Verifier que le certificat est valide</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>RobustnessCertificate<span class=\"bp\">.</span>isValid<span class=\"w\"> </span>(cert<span class=\"w\"> </span>:<span class=\"w\"> </span>RobustnessCertificate)<span class=\"w\"> </span>:<span class=\"w\"> </span><span class=\"kt\">Prop</span><span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>RobustnessCertificate.isValid<span class=\"w\"> </span>(cert<span class=\"w\"> </span>:<span class=\"w\"> </span>RobustnessCertificate)<span class=\"w\"> </span>:<span class=\"w\"> </span><span class=\"kt\">Prop</span><span class=\"w\"> </span>:=</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"c1\">-- La classe prédite doit avoir un score &gt; tous les autres</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">∀</span><span class=\"w\"> </span>(j<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat),<span class=\"w\"> </span>j<span class=\"w\"> </span><span class=\"bp\">≠</span><span class=\"w\"> </span>cert<span class=\"bp\">.</span>predictedClass<span class=\"w\"> </span><span class=\"bp\">→</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    cert<span class=\"bp\">.</span>lowerBounds[cert<span class=\"bp\">.</span>predictedClass]<span class=\"bp\">!</span><span class=\"w\"> </span><span class=\"bp\">&gt;</span><span class=\"w\"> </span>cert<span class=\"bp\">.</span>lowerBounds[j]<span class=\"bp\">!</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">∀</span><span class=\"w\"> </span>(j<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat),<span class=\"w\"> </span>j<span class=\"w\"> </span><span class=\"bp\">≠</span><span class=\"w\"> </span>cert.predictedClass<span class=\"w\"> </span><span class=\"bp\">→</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    cert.lowerBounds[cert.predictedClass]<span class=\"bp\">!</span><span class=\"w\"> </span><span class=\"bp\">&gt;</span><span class=\"w\"> </span>cert.lowerBounds[j]<span class=\"bp\">!</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : certificat pour un &#39;7&#39; de MNIST</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>mnistCertificate<span class=\"w\"> </span>:<span class=\"w\"> </span>RobustnessCertificate<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>inputCenter<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.5</span><span class=\"w\">  </span><span class=\"c1\">-- Valeur fictive</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.01</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : certificat pour un '7' de MNIST</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>mnistCertificate<span class=\"w\"> </span>:<span class=\"w\"> </span>RobustnessCertificate<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>inputCenter<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span><span class=\"w\">  </span><span class=\"c1\">-- Valeur fictive</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">01</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    predictedClass<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">7</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    lowerBounds<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">#</span>[<span class=\"mf\">0.1</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">0.2</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">0.1</span>,<span class=\"w\"> </span><span class=\"mf\">0.3</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">5.0</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">0.1</span>]</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    lowerBounds<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">#</span>[<span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">1</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">1</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">3</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">5</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">1</span>]</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    <span class=\"c1\">-- Classe 7 a score 5.0, meilleur que toutes les autres</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk15\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk15\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Certificat de robustesse defini pour classe 7&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Certificat de robustesse defini pour classe 7&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk17\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk17\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Certificat de robustesse defini pour classe 7\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Certificat de robustesse defini pour classe 7\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 7</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -4123,10 +4108,10 @@
    "id": "interpretation-certificate",
    "metadata": {
     "papermill": {
-     "duration": 0.010161,
-     "end_time": "2026-06-18T03:11:12.981252+00:00",
+     "duration": 0.027712,
+     "end_time": "2026-10-09T15:38:36.135486+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.971091+00:00",
+     "start_time": "2026-10-09T15:38:36.107774+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4161,16 +4146,16 @@
    "id": "crown-comparison",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:13.003745Z",
-     "iopub.status.busy": "2026-06-18T03:11:13.003533Z",
-     "iopub.status.idle": "2026-06-18T03:11:13.143889Z",
-     "shell.execute_reply": "2026-06-18T03:11:13.143153Z"
+     "iopub.execute_input": "2026-10-09T15:38:36.200246Z",
+     "iopub.status.busy": "2026-10-09T15:38:36.200051Z",
+     "iopub.status.idle": "2026-10-09T15:38:36.415245Z",
+     "shell.execute_reply": "2026-10-09T15:38:36.413535Z"
     },
     "papermill": {
-     "duration": 0.152745,
-     "end_time": "2026-06-18T03:11:13.144706+00:00",
+     "duration": 0.247634,
+     "end_time": "2026-10-09T15:38:36.416906+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:12.991961+00:00",
+     "start_time": "2026-10-09T15:38:36.169272+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4193,33 +4178,33 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Resultat de verification</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (method<span class=\"w\"> </span>:<span class=\"w\"> </span>String)<span class=\"w\">  </span><span class=\"c1\">-- &quot;IBP&quot; ou &quot;CROWN&quot;</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span>where</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (method<span class=\"w\"> </span>:<span class=\"w\"> </span>String)<span class=\"w\">  </span><span class=\"c1\">-- \"IBP\" ou \"CROWN\"</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (epsilon<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\">  </span><span class=\"c1\">-- Rayon certifie</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (computationTime<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\">  </span><span class=\"c1\">-- Secondes</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : meme reseau, differentes methodes</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>ibpResult<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;IBP&quot;</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.03</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.5</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>ibpResult<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"IBP\"</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">03</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">5</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>crownResult<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;CROWN&quot;</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.08</span><span class=\"w\">  </span><span class=\"c1\">-- Meilleure borne</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.3</span><span class=\"w\">  </span><span class=\"c1\">-- Plus lent</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>crownResult<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"CROWN\"</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">08</span><span class=\"w\">  </span><span class=\"c1\">-- Meilleure borne</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">3</span><span class=\"w\">  </span><span class=\"c1\">-- Plus lent</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk16\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk16\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>ibpResult</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;IBP&quot;</span>,<span class=\"w\"> </span>epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.030000</span>,<span class=\"w\"> </span>computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.500000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk17\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk17\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>crownResult</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;CROWN&quot;</span>,<span class=\"w\"> </span>epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.080000</span>,<span class=\"w\"> </span>computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.300000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk18\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk18\"><span class=\"k\">#eval</span><span class=\"w\"> </span>ibpResult</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"IBP\"</span>,<span class=\"w\"> </span>epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">030000</span>,<span class=\"w\"> </span>computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">500000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk19\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk19\"><span class=\"k\">#eval</span><span class=\"w\"> </span>crownResult</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>method<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"CROWN\"</span>,<span class=\"w\"> </span>epsilon<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">080000</span>,<span class=\"w\"> </span>computationTime<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">300000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Calcul du ratio d&#39;amelioration</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>improvementRatio<span class=\"w\"> </span>(ibp<span class=\"w\"> </span>crown<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  crown<span class=\"bp\">.</span>epsilon<span class=\"w\"> </span><span class=\"bp\">/</span><span class=\"w\"> </span>ibp<span class=\"bp\">.</span>epsilon</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Calcul du ratio d'amelioration</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>improvementRatio<span class=\"w\"> </span>(ibp<span class=\"w\"> </span>crown<span class=\"w\"> </span>:<span class=\"w\"> </span>VerificationResult)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  crown.epsilon<span class=\"w\"> </span><span class=\"bp\">/</span><span class=\"w\"> </span>ibp.epsilon</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk18\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk18\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>improvementRatio<span class=\"w\"> </span>ibpResult<span class=\"w\"> </span>crownResult<span class=\"w\">  </span><span class=\"c1\">-- ≈ 2.67x</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">2.666667</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1a\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1a\"><span class=\"k\">#eval</span><span class=\"w\"> </span>improvementRatio<span class=\"w\"> </span>ibpResult<span class=\"w\"> </span>crownResult<span class=\"w\">  </span><span class=\"c1\">-- ≈ 2.67x</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">666667</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 8</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -4350,10 +4335,10 @@
    "id": "interpretation-methods-comparison",
    "metadata": {
     "papermill": {
-     "duration": 0.009993,
-     "end_time": "2026-06-18T03:11:13.165415+00:00",
+     "duration": 0.029377,
+     "end_time": "2026-10-09T15:38:36.475929+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.155422+00:00",
+     "start_time": "2026-10-09T15:38:36.446552+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4405,10 +4390,10 @@
    "id": "applications-table",
    "metadata": {
     "papermill": {
-     "duration": 0.011512,
-     "end_time": "2026-06-18T03:11:13.191642+00:00",
+     "duration": 0.039351,
+     "end_time": "2026-10-09T15:38:36.542368+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.180130+00:00",
+     "start_time": "2026-10-09T15:38:36.503017+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4431,16 +4416,16 @@
    "id": "python-integration",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:13.219653Z",
-     "iopub.status.busy": "2026-06-18T03:11:13.219465Z",
-     "iopub.status.idle": "2026-06-18T03:11:13.391406Z",
-     "shell.execute_reply": "2026-06-18T03:11:13.390516Z"
+     "iopub.execute_input": "2026-10-09T15:38:36.614081Z",
+     "iopub.status.busy": "2026-10-09T15:38:36.613798Z",
+     "iopub.status.idle": "2026-10-09T15:38:36.840224Z",
+     "shell.execute_reply": "2026-10-09T15:38:36.839053Z"
     },
     "papermill": {
-     "duration": 0.186217,
-     "end_time": "2026-06-18T03:11:13.391992+00:00",
+     "duration": 0.263482,
+     "end_time": "2026-10-09T15:38:36.840958+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.205775+00:00",
+     "start_time": "2026-10-09T15:38:36.577476+00:00",
      "status": "completed"
     },
     "tags": []
@@ -4463,13 +4448,13 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- ===========================================================</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Type de modele exportable</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>ExportableModel<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>ExportableModel<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (layers<span class=\"w\"> </span>:<span class=\"w\"> </span>List<span class=\"w\"> </span>Module)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (verificationResults<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>VerificationResult)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Metadata pour l&#39;export</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">structure</span><span class=\"w\"> </span>ExportMetadata<span class=\"w\"> </span><span class=\"kn\">where</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Metadata pour l'export</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">structure</span><span class=\"w\"> </span>ExportMetadata<span class=\"w\"> </span>where</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (modelName<span class=\"w\"> </span>:<span class=\"w\"> </span>String)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (leanVersion<span class=\"w\"> </span>:<span class=\"w\"> </span>String)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  (torchleanVersion<span class=\"w\"> </span>:<span class=\"w\"> </span>String)</span></span></pre>\n",
@@ -4477,19 +4462,19 @@
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  deriving<span class=\"w\"> </span>Repr</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exemple : modele verifie a exporter</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>verifiedMLP<span class=\"w\"> </span>:<span class=\"w\"> </span>ExportableModel<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>layers<span class=\"w\"> </span>:=<span class=\"w\"> </span>[Module<span class=\"bp\">.</span>linear<span class=\"w\"> </span>mnistLayer,<span class=\"w\"> </span>Module<span class=\"bp\">.</span>relu]</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>verifiedMLP<span class=\"w\"> </span>:<span class=\"w\"> </span>ExportableModel<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>layers<span class=\"w\"> </span>:=<span class=\"w\"> </span>[Module.linear<span class=\"w\"> </span>mnistLayer,<span class=\"w\"> </span>Module.relu]</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    verificationResults<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">#</span>[ibpResult,<span class=\"w\"> </span>crownResult]</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>metadata<span class=\"w\"> </span>:<span class=\"w\"> </span>ExportMetadata<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>modelName<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;MNIST_Verified&quot;</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    leanVersion<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;v4.0.0&quot;</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    torchleanVersion<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;0.1.0&quot;</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    verificationDate<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">&quot;2026-03-03&quot;</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>metadata<span class=\"w\"> </span>:<span class=\"w\"> </span>ExportMetadata<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  {<span class=\"w\"> </span>modelName<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"MNIST_Verified\"</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    leanVersion<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"v4.0.0\"</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    torchleanVersion<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"0.1.0\"</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    verificationDate<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"s2\">\"2026-03-03\"</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  }</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk19\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk19\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span><span class=\"s2\">&quot;Modele verifiable prepare pour export Python&quot;</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">&quot;Modele verifiable prepare pour export Python&quot;</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1b\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1b\"><span class=\"k\">#eval</span><span class=\"w\"> </span><span class=\"s2\">\"Modele verifiable prepare pour export Python\"</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"s2\">\"Modele verifiable prepare pour export Python\"</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 9</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
@@ -4598,10 +4583,10 @@
    "id": "interpretation-python-integration",
    "metadata": {
     "papermill": {
-     "duration": 0.010521,
-     "end_time": "2026-06-18T03:11:13.413723+00:00",
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      "exception": false,
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      "status": "completed"
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     "tags": []
@@ -4760,96 +4745,7 @@
     "  unfold roundExample\n",
     "  cases x\n",
     "  all_goals simp [h]\n",
-    "```\n",
-    "\n",
-    "***\n",
-    "\n",
-    "### Exercice (à compléter) : Borne IBP sur une couche à poids négatif\n",
-    "\n",
-    "Réutilisez les fonctions `linearIBP` et `reluIBP` de l'**exemple guidé 1** pour propager un intervalle à travers une couche **à poids négatif** suivie d'un ReLU.\n",
-    "\n",
-    "- Input : `x ∈ [-1.0, 2.0]`\n",
-    "- Layer : `weight = -3.0, bias = 1.0`\n",
-    "- Puis : `ReLU`\n",
-    "\n",
-    "**Question** : Quel est l'intervalle de sortie ? Attention au cas `w < 0` (les bornes inférieure et supérieure s'inversent).\n",
-    "\n",
-    "```lean\n",
-    "-- A completer : utilisez linearIBP puis reluIBP (définies dans l'exemple guidé 1)\n",
-    "-- Indice : pour w < 0, linearIBP inverse lower et upper\n",
-    "def exoLibre_input  : Interval := { lower := -1.0, upper := 2.0 }\n",
-    "def exoLibre_layer  : Interval := sorry  -- TODO etudiant\n",
-    "def exoLibre_output : Interval := sorry  -- TODO etudiant\n",
-    "\n",
-    "-- #eval exoLibre_layer\n",
-    "-- #eval exoLibre_output\n",
-    "```\n",
-    "\n",
-    "***\n",
-    "\n",
-    "<a id=\"8-conclusion\"></a>\n",
-    "\n",
-    "## 8. Conclusion\n",
-    "\n",
-    "### 8.1 Récapitulatif\n",
-    "\n",
-    "Dans ce notebook, nous avons vu :\n",
-    "\n",
-    "| Concept | Appris | Application |\n",
-    "|---------|--------|-------------|\n",
-    "| **Semantic gap** | Différence PyTorch vs formel | Comprendre les limites de PyTorch |\n",
-    "| **TorchLean** | Architecture 3 modules | Installation et imports |\n",
-    "| **API** | Tenseurs, layers, sequential | Construction de réseaux |\n",
-    "| **Float32** | IEEE-754, arrondi | Preuves d'erreur numérique |\n",
-    "| **IBP** | Propagation d'intervalles | Bornes rapides |\n",
-    "| **CROWN** | Optimisation convexe | Bornes serrées |\n",
-    "| **Applications** | PINNs, Lyapunov | Cas réels |\n",
-    "\n",
-    "### 8.2 Tableau comparatif final\n",
-    "\n",
-    "| Approche | Vérification | Performance | Scalabilité | Garanties |\n",
-    "|----------|---------------|--------------|-------------|-----------|\n",
-    "| **PyTorch** | Tests empiriques | Maximale | Oui | Statistiques seulement |\n",
-    "| **TorchLean IBP** | Formelle | Bonne | Oui | Conservatrices |\n",
-    "| **TorchLean CROWN** | Formelle | Moyenne | Oui | Serrées |\n",
-    "| **SMT solving** | Formelle | Faible | Non | Exactes mais coûteuses |\n",
-    "\n",
-    "### 8.3 Ressources supplémentaires\n",
-    "\n",
-    "**TorchLean** :\n",
-    "- Site officiel : [leandojo.org/torchlean.html](https://leandojo.org/torchlean.html)\n",
-    "- GitHub : [github.com/lean-dojo/TorchLean](https://github.com/lean-dojo/TorchLean)\n",
-    "\n",
-    "**Vérification de réseaux** :\n",
-    "- IBP original : Gowal et al. (2018)\n",
-    "- CROWN : Singh et al. (2019)\n",
-    "- LiRPA : Xu et al. (2020)\n",
-    "\n",
-    "**Lean 4** :\n",
-    "- [Theorem Proving in Lean 4](https://leanprover.github.io/theorem_proving_in_lean4/)\n",
-    "- [Mathematics in Lean](https://leanprover-community.github.io/mathematics_in_lean/)\n",
-    "\n",
-    "### 8.4 Prochains pas\n",
-    "\n",
-    "Après ce notebook, vous pouvez :\n",
-    "\n",
-    "1. **Approfondir TorchLean** : Expérimenter avec des réseaux réels\n",
-    "2. **Lean-12** : Applications avancées de TorchLean (si disponible)\n",
-    "3. **Contribuer** : Au projet TorchLean sur GitHub\n",
-    "4. **Recherche** : Explorer PINNs vérifiés, contrôle formel\n",
-    "\n",
-    "### 8.5 Note sur l'état du projet\n",
-    "\n",
-    "TorchLean est un projet de recherche actif. Certains composants décrits dans ce notebook peuvent être :\n",
-    "- En cours de développement\n",
-    "- Sujets à modifications API\n",
-    "- Partiellement implémentés\n",
-    "\n",
-    "Consultez toujours la documentation officielle pour l'état actuel.\n",
-    "\n",
-    "***\n",
-    "\n",
-    "**Navigation** : [Index](README.md) | [<< Précédent](Lean-10-LeanDojo.ipynb) | [Version Python](Lean-11b-TorchLean-Python.ipynb) | [Lean-12 Sensitivity >>](Lean-12-Sensitivity-Theorem.ipynb)"
+    "```\n"
    ]
   },
   {
@@ -4857,10 +4753,10 @@
    "id": "e51f9628",
    "metadata": {
     "papermill": {
-     "duration": 0.011497,
-     "end_time": "2026-06-18T03:11:13.437146+00:00",
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      "status": "completed"
     },
     "tags": []
@@ -4883,16 +4779,16 @@
    "id": "52ca464c",
    "metadata": {
     "execution": {
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-     "iopub.status.idle": "2026-06-18T03:11:13.577972Z",
-     "shell.execute_reply": "2026-06-18T03:11:13.577124Z"
+     "iopub.execute_input": "2026-10-09T15:38:37.062537Z",
+     "iopub.status.busy": "2026-10-09T15:38:37.062329Z",
+     "iopub.status.idle": "2026-10-09T15:38:37.251472Z",
+     "shell.execute_reply": "2026-10-09T15:38:37.249519Z"
     },
     "papermill": {
-     "duration": 0.13039,
-     "end_time": "2026-06-18T03:11:13.578452+00:00",
+     "duration": 0.226139,
+     "end_time": "2026-10-09T15:38:37.252485+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.448062+00:00",
+     "start_time": "2026-10-09T15:38:37.026346+00:00",
      "status": "completed"
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     "tags": []
@@ -4912,24 +4808,24 @@
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exercice 1 : propagation IBP à travers une couche à poids négatif puis ReLU.</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Réutilise `Interval` et `reluIBP` définis plus haut (section 5, IBP).</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Seul `linearIBP` est (re)défini ici (il n&#39;apparaît que dans l&#39;exemple guidé 1).</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>linearIBP<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>(w<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(b<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Seul `linearIBP` est (re)défini ici (il n'apparaît que dans l'exemple guidé 1).</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>linearIBP<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval)<span class=\"w\"> </span>(w<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(b<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">≥</span><span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\"> </span><span class=\"k\">then</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>lower<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>upper<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b<span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.lower<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.upper<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>upper<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i<span class=\"bp\">.</span>lower<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b<span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">    {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.upper<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span>i.lower<span class=\"w\"> </span><span class=\"bp\">*</span><span class=\"w\"> </span>w<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span>b<span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- TODO étudiant : calculez la borne après Linear(w = -3.0, b = 1.0) puis ReLU.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo1_input<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mf\">1.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">2.0</span><span class=\"w\"> </span>}</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo1_layer<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo1_input (-3.0) 1.0</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo1_output<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>exo1_layer</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo1_input<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo1_layer<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo1_input (-3.0) 1.0</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo1_output<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>exo1_layer</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1a\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1a\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>exo1_output<span class=\"w\">  </span><span class=\"c1\">-- solution attendue : { lower := 0.0, upper := 4.0 }</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1c\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1c\"><span class=\"k\">#eval</span><span class=\"w\"> </span>exo1_output</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 10</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
        "            <summary>Raw input</summary>\n",
-       "            <code>{\"cmd\": \"-- Exercice 1 : propagation IBP \\u00e0 travers une couche \\u00e0 poids n\\u00e9gatif puis ReLU.\\n-- R\\u00e9utilise `Interval` et `reluIBP` d\\u00e9finis plus haut (section 5, IBP).\\n-- Seul `linearIBP` est (re)d\\u00e9fini ici (il n'appara\\u00eet que dans l'exemple guid\\u00e9 1).\\ndef linearIBP (i : Interval) (w : Float) (b : Float) : Interval :=\\n  if w \\u2265 0 then\\n    { lower := i.lower * w + b, upper := i.upper * w + b }\\n  else\\n    { lower := i.upper * w + b, upper := i.lower * w + b }\\n\\n-- TODO \\u00e9tudiant : calculez la borne apr\\u00e8s Linear(w = -3.0, b = 1.0) puis ReLU.\\ndef exo1_input  : Interval := { lower := -1.0, upper := 2.0 }\\ndef exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo1_input (-3.0) 1.0\\ndef exo1_output : Interval := reluIBP exo1_layer\\n\\n#eval exo1_output  -- solution attendue : { lower := 0.0, upper := 4.0 }\", \"env\": 9}</code>\n",
+       "            <code>{\"cmd\": \"-- Exercice 1 : propagation IBP \\u00e0 travers une couche \\u00e0 poids n\\u00e9gatif puis ReLU.\\n-- R\\u00e9utilise `Interval` et `reluIBP` d\\u00e9finis plus haut (section 5, IBP).\\n-- Seul `linearIBP` est (re)d\\u00e9fini ici (il n'appara\\u00eet que dans l'exemple guid\\u00e9 1).\\ndef linearIBP (i : Interval) (w : Float) (b : Float) : Interval :=\\n  if w \\u2265 0 then\\n    { lower := i.lower * w + b, upper := i.upper * w + b }\\n  else\\n    { lower := i.upper * w + b, upper := i.lower * w + b }\\n\\n-- TODO \\u00e9tudiant : calculez la borne apr\\u00e8s Linear(w = -3.0, b = 1.0) puis ReLU.\\ndef exo1_input  : Interval := { lower := -1.0, upper := 2.0 }\\ndef exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo1_input (-3.0) 1.0\\ndef exo1_output : Interval := reluIBP exo1_layer\\n\\n#eval exo1_output\", \"env\": 9}</code>\n",
        "        </details>\n",
        "        <details>\n",
        "            <summary>Raw output</summary>\n",
@@ -4957,12 +4853,12 @@
        "def exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO étudiant : linearIBP exo1_input (-3.0) 1.0\n",
        "def exo1_output : Interval := reluIBP exo1_layer\n",
        "\n",
-       "#eval exo1_output  -- solution attendue : { lower := 0.0, upper := 4.0 }\n",
+       "#eval exo1_output\n",
        "─────▶  { lower := 0.000000, upper := 0.000000 }\n",
        "--% env 10\n",
        "\n",
        "Raw input:\n",
-       "{\"cmd\": \"-- Exercice 1 : propagation IBP \\u00e0 travers une couche \\u00e0 poids n\\u00e9gatif puis ReLU.\\n-- R\\u00e9utilise `Interval` et `reluIBP` d\\u00e9finis plus haut (section 5, IBP).\\n-- Seul `linearIBP` est (re)d\\u00e9fini ici (il n'appara\\u00eet que dans l'exemple guid\\u00e9 1).\\ndef linearIBP (i : Interval) (w : Float) (b : Float) : Interval :=\\n  if w \\u2265 0 then\\n    { lower := i.lower * w + b, upper := i.upper * w + b }\\n  else\\n    { lower := i.upper * w + b, upper := i.lower * w + b }\\n\\n-- TODO \\u00e9tudiant : calculez la borne apr\\u00e8s Linear(w = -3.0, b = 1.0) puis ReLU.\\ndef exo1_input  : Interval := { lower := -1.0, upper := 2.0 }\\ndef exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo1_input (-3.0) 1.0\\ndef exo1_output : Interval := reluIBP exo1_layer\\n\\n#eval exo1_output  -- solution attendue : { lower := 0.0, upper := 4.0 }\", \"env\": 9}\n",
+       "{\"cmd\": \"-- Exercice 1 : propagation IBP \\u00e0 travers une couche \\u00e0 poids n\\u00e9gatif puis ReLU.\\n-- R\\u00e9utilise `Interval` et `reluIBP` d\\u00e9finis plus haut (section 5, IBP).\\n-- Seul `linearIBP` est (re)d\\u00e9fini ici (il n'appara\\u00eet que dans l'exemple guid\\u00e9 1).\\ndef linearIBP (i : Interval) (w : Float) (b : Float) : Interval :=\\n  if w \\u2265 0 then\\n    { lower := i.lower * w + b, upper := i.upper * w + b }\\n  else\\n    { lower := i.upper * w + b, upper := i.lower * w + b }\\n\\n-- TODO \\u00e9tudiant : calculez la borne apr\\u00e8s Linear(w = -3.0, b = 1.0) puis ReLU.\\ndef exo1_input  : Interval := { lower := -1.0, upper := 2.0 }\\ndef exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo1_input (-3.0) 1.0\\ndef exo1_output : Interval := reluIBP exo1_layer\\n\\n#eval exo1_output\", \"env\": 9}\n",
        "Raw output:\n",
        "{\"messages\":\r\n",
        " [{\"severity\": \"info\",\r\n",
@@ -4991,7 +4887,7 @@
     "def exo1_layer  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO étudiant : linearIBP exo1_input (-3.0) 1.0\n",
     "def exo1_output : Interval := reluIBP exo1_layer\n",
     "\n",
-    "#eval exo1_output  -- solution attendue : { lower := 0.0, upper := 4.0 }"
+    "#eval exo1_output"
    ]
   },
   {
@@ -4999,10 +4895,10 @@
    "id": "bb99dc9b",
    "metadata": {
     "papermill": {
-     "duration": 0.009833,
-     "end_time": "2026-06-18T03:11:13.598785+00:00",
+     "duration": 0.031135,
+     "end_time": "2026-10-09T15:38:37.311699+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.588952+00:00",
+     "start_time": "2026-10-09T15:38:37.280564+00:00",
      "status": "completed"
     },
     "tags": []
@@ -5019,16 +4915,16 @@
    "id": "ee293686",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:13.620932Z",
-     "iopub.status.busy": "2026-06-18T03:11:13.620777Z",
-     "iopub.status.idle": "2026-06-18T03:11:14.419099Z",
-     "shell.execute_reply": "2026-06-18T03:11:14.417518Z"
+     "iopub.execute_input": "2026-10-09T15:38:37.379400Z",
+     "iopub.status.busy": "2026-10-09T15:38:37.379221Z",
+     "iopub.status.idle": "2026-10-09T15:38:38.475200Z",
+     "shell.execute_reply": "2026-10-09T15:38:38.474040Z"
     },
     "papermill": {
-     "duration": 0.810165,
-     "end_time": "2026-06-18T03:11:14.419679+00:00",
+     "duration": 1.130482,
+     "end_time": "2026-10-09T15:38:38.476136+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:13.609514+00:00",
+     "start_time": "2026-10-09T15:38:37.345654+00:00",
      "status": "completed"
     },
     "tags": []
@@ -5047,31 +4943,31 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exercice 2 : classe certifiée et marge de robustesse.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>argmax<span class=\"w\"> </span>(scores<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(bestIdx<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"w\"> </span><span class=\"bp\">&gt;=</span><span class=\"w\"> </span>scores<span class=\"bp\">.</span>size<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>bestIdx</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>argmax<span class=\"w\"> </span>(scores<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(bestIdx<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"w\"> </span><span class=\"bp\">&gt;=</span><span class=\"w\"> </span>scores.size<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>bestIdx</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>scores[i]<span class=\"bp\">!</span><span class=\"w\"> </span><span class=\"bp\">&gt;</span><span class=\"w\"> </span>scores[bestIdx]<span class=\"bp\">!</span><span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>argmax<span class=\"w\"> </span>scores<span class=\"w\"> </span>(i<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span>)<span class=\"w\"> </span>i</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span>argmax<span class=\"w\"> </span>scores<span class=\"w\"> </span>(i<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span>)<span class=\"w\"> </span>bestIdx</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>secondBest<span class=\"w\"> </span>(scores<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(bestIdx<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(best2<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"w\"> </span><span class=\"bp\">&gt;=</span><span class=\"w\"> </span>scores<span class=\"bp\">.</span>size<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>best2</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>secondBest<span class=\"w\"> </span>(scores<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float)<span class=\"w\"> </span>(bestIdx<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(i<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat)<span class=\"w\"> </span>(best2<span class=\"w\"> </span>:<span class=\"w\"> </span>Float)<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"w\"> </span><span class=\"bp\">&gt;=</span><span class=\"w\"> </span>scores.size<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>best2</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span><span class=\"k\">if</span><span class=\"w\"> </span>i<span class=\"w\"> </span><span class=\"bp\">==</span><span class=\"w\"> </span>bestIdx<span class=\"w\"> </span><span class=\"k\">then</span><span class=\"w\"> </span>secondBest<span class=\"w\"> </span>scores<span class=\"w\"> </span>bestIdx<span class=\"w\"> </span>(i<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span>)<span class=\"w\"> </span>best2</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"k\">else</span><span class=\"w\"> </span>secondBest<span class=\"w\"> </span>scores<span class=\"w\"> </span>bestIdx<span class=\"w\"> </span>(i<span class=\"w\"> </span><span class=\"bp\">+</span><span class=\"w\"> </span><span class=\"mi\">1</span>)<span class=\"w\"> </span>(max<span class=\"w\"> </span>best2<span class=\"w\"> </span>scores[i]<span class=\"bp\">!</span>)</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo2_bounds<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">#</span>[<span class=\"mf\">0.1</span>,<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mf\">0.2</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">0.3</span>,<span class=\"w\"> </span><span class=\"mf\">0.05</span>,<span class=\"w\"> </span><span class=\"mf\">0.4</span>,<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span><span class=\"mf\">2.5</span>,<span class=\"w\"> </span><span class=\"mf\">0.1</span>,<span class=\"w\"> </span><span class=\"mf\">0.2</span>]</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo2_bounds<span class=\"w\"> </span>:<span class=\"w\"> </span>Array<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\">  <span class=\"bp\">#</span>[<span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">1</span>,<span class=\"w\"> </span><span class=\"bp\">-</span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">2</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">3</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">05</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">4</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span><span class=\"mi\">2</span><span class=\"bp\">.</span><span class=\"mi\">5</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">1</span>,<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">2</span>]</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- TODO étudiant : classe certifiée (indice : argmax exo2_bounds 1 0)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo2_certified<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo2_certified<span class=\"w\"> </span>:<span class=\"w\"> </span>Nat<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- TODO étudiant : marge = best - second (indice : secondBest exo2_bounds ...)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo2_margin<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo2_margin<span class=\"w\"> </span>:<span class=\"w\"> </span>Float<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant</span></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1b\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1b\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>exo2_certified<span class=\"w\">  </span><span class=\"c1\">-- solution attendue : 7</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">0</span></blockquote></div></div></small></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1c\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1c\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>exo2_margin<span class=\"w\">     </span><span class=\"c1\">-- solution attendue : 2.1</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mf\">0.000000</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1d\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1d\"><span class=\"k\">#eval</span><span class=\"w\"> </span>exo2_certified</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">0</span></blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1e\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1e\"><span class=\"k\">#eval</span><span class=\"w\"> </span>exo2_margin</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> <span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span></blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 11</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
        "            <summary>Raw input</summary>\n",
-       "            <code>{\"cmd\": \"-- Exercice 2 : classe certifi\\u00e9e et marge de robustesse.\\ndef argmax (scores : Array Float) (i : Nat) (bestIdx : Nat) : Nat :=\\n  if i >= scores.size then bestIdx\\n  else if scores[i]! > scores[bestIdx]! then argmax scores (i + 1) i\\n  else argmax scores (i + 1) bestIdx\\n\\ndef secondBest (scores : Array Float) (bestIdx : Nat) (i : Nat) (best2 : Float) : Float :=\\n  if i >= scores.size then best2\\n  else if i == bestIdx then secondBest scores bestIdx (i + 1) best2\\n  else secondBest scores bestIdx (i + 1) (max best2 scores[i]!)\\n\\ndef exo2_bounds : Array Float :=\\n  #[0.1, -0.2, 0.0, 0.3, 0.05, 0.4, 0.0, 2.5, 0.1, 0.2]\\n\\n-- TODO \\u00e9tudiant : classe certifi\\u00e9e (indice : argmax exo2_bounds 1 0)\\ndef exo2_certified : Nat := 0  -- TODO \\u00e9tudiant\\n-- TODO \\u00e9tudiant : marge = best - second (indice : secondBest exo2_bounds ...)\\ndef exo2_margin : Float := 0.0  -- TODO \\u00e9tudiant\\n\\n#eval exo2_certified  -- solution attendue : 7\\n#eval exo2_margin     -- solution attendue : 2.1\", \"env\": 10}</code>\n",
+       "            <code>{\"cmd\": \"-- Exercice 2 : classe certifi\\u00e9e et marge de robustesse.\\ndef argmax (scores : Array Float) (i : Nat) (bestIdx : Nat) : Nat :=\\n  if i >= scores.size then bestIdx\\n  else if scores[i]! > scores[bestIdx]! then argmax scores (i + 1) i\\n  else argmax scores (i + 1) bestIdx\\n\\ndef secondBest (scores : Array Float) (bestIdx : Nat) (i : Nat) (best2 : Float) : Float :=\\n  if i >= scores.size then best2\\n  else if i == bestIdx then secondBest scores bestIdx (i + 1) best2\\n  else secondBest scores bestIdx (i + 1) (max best2 scores[i]!)\\n\\ndef exo2_bounds : Array Float :=\\n  #[0.1, -0.2, 0.0, 0.3, 0.05, 0.4, 0.0, 2.5, 0.1, 0.2]\\n\\n-- TODO \\u00e9tudiant : classe certifi\\u00e9e (indice : argmax exo2_bounds 1 0)\\ndef exo2_certified : Nat := 0  -- TODO \\u00e9tudiant\\n-- TODO \\u00e9tudiant : marge = best - second (indice : secondBest exo2_bounds ...)\\ndef exo2_margin : Float := 0.0  -- TODO \\u00e9tudiant\\n\\n#eval exo2_certified\\n#eval exo2_margin\", \"env\": 10}</code>\n",
        "        </details>\n",
        "        <details>\n",
        "            <summary>Raw output</summary>\n",
@@ -5108,14 +5004,14 @@
        "-- TODO étudiant : marge = best - second (indice : secondBest exo2_bounds ...)\n",
        "def exo2_margin : Float := 0.0  -- TODO étudiant\n",
        "\n",
-       "#eval exo2_certified  -- solution attendue : 7\n",
+       "#eval exo2_certified\n",
        "─────▶  0\n",
-       "#eval exo2_margin     -- solution attendue : 2.1\n",
+       "#eval exo2_margin\n",
        "─────▶  0.000000\n",
        "--% env 11\n",
        "\n",
        "Raw input:\n",
-       "{\"cmd\": \"-- Exercice 2 : classe certifi\\u00e9e et marge de robustesse.\\ndef argmax (scores : Array Float) (i : Nat) (bestIdx : Nat) : Nat :=\\n  if i >= scores.size then bestIdx\\n  else if scores[i]! > scores[bestIdx]! then argmax scores (i + 1) i\\n  else argmax scores (i + 1) bestIdx\\n\\ndef secondBest (scores : Array Float) (bestIdx : Nat) (i : Nat) (best2 : Float) : Float :=\\n  if i >= scores.size then best2\\n  else if i == bestIdx then secondBest scores bestIdx (i + 1) best2\\n  else secondBest scores bestIdx (i + 1) (max best2 scores[i]!)\\n\\ndef exo2_bounds : Array Float :=\\n  #[0.1, -0.2, 0.0, 0.3, 0.05, 0.4, 0.0, 2.5, 0.1, 0.2]\\n\\n-- TODO \\u00e9tudiant : classe certifi\\u00e9e (indice : argmax exo2_bounds 1 0)\\ndef exo2_certified : Nat := 0  -- TODO \\u00e9tudiant\\n-- TODO \\u00e9tudiant : marge = best - second (indice : secondBest exo2_bounds ...)\\ndef exo2_margin : Float := 0.0  -- TODO \\u00e9tudiant\\n\\n#eval exo2_certified  -- solution attendue : 7\\n#eval exo2_margin     -- solution attendue : 2.1\", \"env\": 10}\n",
+       "{\"cmd\": \"-- Exercice 2 : classe certifi\\u00e9e et marge de robustesse.\\ndef argmax (scores : Array Float) (i : Nat) (bestIdx : Nat) : Nat :=\\n  if i >= scores.size then bestIdx\\n  else if scores[i]! > scores[bestIdx]! then argmax scores (i + 1) i\\n  else argmax scores (i + 1) bestIdx\\n\\ndef secondBest (scores : Array Float) (bestIdx : Nat) (i : Nat) (best2 : Float) : Float :=\\n  if i >= scores.size then best2\\n  else if i == bestIdx then secondBest scores bestIdx (i + 1) best2\\n  else secondBest scores bestIdx (i + 1) (max best2 scores[i]!)\\n\\ndef exo2_bounds : Array Float :=\\n  #[0.1, -0.2, 0.0, 0.3, 0.05, 0.4, 0.0, 2.5, 0.1, 0.2]\\n\\n-- TODO \\u00e9tudiant : classe certifi\\u00e9e (indice : argmax exo2_bounds 1 0)\\ndef exo2_certified : Nat := 0  -- TODO \\u00e9tudiant\\n-- TODO \\u00e9tudiant : marge = best - second (indice : secondBest exo2_bounds ...)\\ndef exo2_margin : Float := 0.0  -- TODO \\u00e9tudiant\\n\\n#eval exo2_certified\\n#eval exo2_margin\", \"env\": 10}\n",
        "Raw output:\n",
        "{\"messages\":\r\n",
        " [{\"severity\": \"info\",\r\n",
@@ -5153,8 +5049,8 @@
     "-- TODO étudiant : marge = best - second (indice : secondBest exo2_bounds ...)\n",
     "def exo2_margin : Float := 0.0  -- TODO étudiant\n",
     "\n",
-    "#eval exo2_certified  -- solution attendue : 7\n",
-    "#eval exo2_margin     -- solution attendue : 2.1"
+    "#eval exo2_certified\n",
+    "#eval exo2_margin"
    ]
   },
   {
@@ -5162,10 +5058,10 @@
    "id": "e407f8cc",
    "metadata": {
     "papermill": {
-     "duration": 0.01003,
-     "end_time": "2026-06-18T03:11:14.457731+00:00",
+     "duration": 0.034914,
+     "end_time": "2026-10-09T15:38:38.536850+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:14.447701+00:00",
+     "start_time": "2026-10-09T15:38:38.501936+00:00",
      "status": "completed"
     },
     "tags": []
@@ -5182,16 +5078,16 @@
    "id": "3544712b",
    "metadata": {
     "execution": {
-     "iopub.execute_input": "2026-06-18T03:11:14.479924Z",
-     "iopub.status.busy": "2026-06-18T03:11:14.479772Z",
-     "iopub.status.idle": "2026-06-18T03:11:14.591702Z",
-     "shell.execute_reply": "2026-06-18T03:11:14.590863Z"
+     "iopub.execute_input": "2026-10-09T15:38:38.594495Z",
+     "iopub.status.busy": "2026-10-09T15:38:38.594292Z",
+     "iopub.status.idle": "2026-10-09T15:38:38.755325Z",
+     "shell.execute_reply": "2026-10-09T15:38:38.754441Z"
     },
     "papermill": {
-     "duration": 0.123656,
-     "end_time": "2026-06-18T03:11:14.592229+00:00",
+     "duration": 0.190702,
+     "end_time": "2026-10-09T15:38:38.755834+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:14.468573+00:00",
+     "start_time": "2026-10-09T15:38:38.565132+00:00",
      "status": "completed"
     },
     "tags": []
@@ -5210,20 +5106,20 @@
        "    \n",
        "        <div class=\"alectryon-root alectryon-centered\">\n",
        "            <pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- Exercice 3 : IBP sur deux couches linéaires + ReLU final.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- (Interval / linearIBP / reluIBP sont définis dans l&#39;exercice 1 ci-dessus.)</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo3_input<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">1.0</span><span class=\"w\"> </span>}</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- (Interval / linearIBP / reluIBP sont définis dans l'exercice 1 ci-dessus.)</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo3_input<span class=\"w\"> </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">1</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">-- TODO étudiant : couche 1 (w = 2.0, b = 0.5), couche 2 (w = -1.0, b = 0.0), puis ReLU.</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo3_after1<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo3_input 2.0 0.5</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo3_after2<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo3_after1 (-1.0) 0.0</span></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kn\">def</span><span class=\"w\"> </span>exo3_output<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>exo3_after2</span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo3_after1<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo3_input 2.0 0.5</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo3_after2<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>{<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">0</span><span class=\"w\"> </span>}<span class=\"w\">  </span><span class=\"c1\">-- TODO étudiant : linearIBP exo3_after1 (-1.0) 0.0</span></span></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"kd\">def</span><span class=\"w\"> </span>exo3_output<span class=\"w\">  </span>:<span class=\"w\"> </span>Interval<span class=\"w\"> </span>:=<span class=\"w\"> </span>reluIBP<span class=\"w\"> </span>exo3_after2</span></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"></span></span></pre>\n",
-       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1d\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1d\"><span class=\"bp\">#</span>eval<span class=\"w\"> </span>exo3_output<span class=\"w\">  </span><span class=\"c1\">-- solution attendue : { lower := 0.0, upper := 2.5 }</span></label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mf\">0.000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
+       "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><input class=\"alectryon-toggle\" id=\"chk1f\" style=\"display: none\" type=\"checkbox\"><label class=\"alectryon-input\" for=\"chk1f\"><span class=\"k\">#eval</span><span class=\"w\"> </span>exo3_output</label><small class=\"alectryon-output\"><div><div class=\"alectryon-messages\"><blockquote class=\"alectryon-message\"> {<span class=\"w\"> </span>lower<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span>,<span class=\"w\"> </span>upper<span class=\"w\"> </span>:=<span class=\"w\"> </span><span class=\"mi\">0</span><span class=\"bp\">.</span><span class=\"mi\">000000</span><span class=\"w\"> </span>}</blockquote></div></div></small></span></pre>\n",
        "<pre class=\"alectryon-io highlight\"><!-- Generator: Alectryon --><span class=\"alectryon-sentence\"><span class=\"alectryon-input\"><span class=\"c1\">--% env 12</span></span></span></pre>\n",
        "        </div>\n",
        "        <details>\n",
        "            <summary>Raw input</summary>\n",
-       "            <code>{\"cmd\": \"-- Exercice 3 : IBP sur deux couches lin\\u00e9aires + ReLU final.\\n-- (Interval / linearIBP / reluIBP sont d\\u00e9finis dans l'exercice 1 ci-dessus.)\\ndef exo3_input : Interval := { lower := 0.0, upper := 1.0 }\\n\\n-- TODO \\u00e9tudiant : couche 1 (w = 2.0, b = 0.5), couche 2 (w = -1.0, b = 0.0), puis ReLU.\\ndef exo3_after1  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_input 2.0 0.5\\ndef exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_after1 (-1.0) 0.0\\ndef exo3_output  : Interval := reluIBP exo3_after2\\n\\n#eval exo3_output  -- solution attendue : { lower := 0.0, upper := 2.5 }\", \"env\": 11}</code>\n",
+       "            <code>{\"cmd\": \"-- Exercice 3 : IBP sur deux couches lin\\u00e9aires + ReLU final.\\n-- (Interval / linearIBP / reluIBP sont d\\u00e9finis dans l'exercice 1 ci-dessus.)\\ndef exo3_input : Interval := { lower := 0.0, upper := 1.0 }\\n\\n-- TODO \\u00e9tudiant : couche 1 (w = 2.0, b = 0.5), couche 2 (w = -1.0, b = 0.0), puis ReLU.\\ndef exo3_after1  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_input 2.0 0.5\\ndef exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_after1 (-1.0) 0.0\\ndef exo3_output  : Interval := reluIBP exo3_after2\\n\\n#eval exo3_output\", \"env\": 11}</code>\n",
        "        </details>\n",
        "        <details>\n",
        "            <summary>Raw output</summary>\n",
@@ -5246,12 +5142,12 @@
        "def exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO étudiant : linearIBP exo3_after1 (-1.0) 0.0\n",
        "def exo3_output  : Interval := reluIBP exo3_after2\n",
        "\n",
-       "#eval exo3_output  -- solution attendue : { lower := 0.0, upper := 2.5 }\n",
+       "#eval exo3_output\n",
        "─────▶  { lower := 0.000000, upper := 0.000000 }\n",
        "--% env 12\n",
        "\n",
        "Raw input:\n",
-       "{\"cmd\": \"-- Exercice 3 : IBP sur deux couches lin\\u00e9aires + ReLU final.\\n-- (Interval / linearIBP / reluIBP sont d\\u00e9finis dans l'exercice 1 ci-dessus.)\\ndef exo3_input : Interval := { lower := 0.0, upper := 1.0 }\\n\\n-- TODO \\u00e9tudiant : couche 1 (w = 2.0, b = 0.5), couche 2 (w = -1.0, b = 0.0), puis ReLU.\\ndef exo3_after1  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_input 2.0 0.5\\ndef exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_after1 (-1.0) 0.0\\ndef exo3_output  : Interval := reluIBP exo3_after2\\n\\n#eval exo3_output  -- solution attendue : { lower := 0.0, upper := 2.5 }\", \"env\": 11}\n",
+       "{\"cmd\": \"-- Exercice 3 : IBP sur deux couches lin\\u00e9aires + ReLU final.\\n-- (Interval / linearIBP / reluIBP sont d\\u00e9finis dans l'exercice 1 ci-dessus.)\\ndef exo3_input : Interval := { lower := 0.0, upper := 1.0 }\\n\\n-- TODO \\u00e9tudiant : couche 1 (w = 2.0, b = 0.5), couche 2 (w = -1.0, b = 0.0), puis ReLU.\\ndef exo3_after1  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_input 2.0 0.5\\ndef exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO \\u00e9tudiant : linearIBP exo3_after1 (-1.0) 0.0\\ndef exo3_output  : Interval := reluIBP exo3_after2\\n\\n#eval exo3_output\", \"env\": 11}\n",
        "Raw output:\n",
        "{\"messages\":\r\n",
        " [{\"severity\": \"info\",\r\n",
@@ -5275,7 +5171,7 @@
     "def exo3_after2  : Interval := { lower := 0.0, upper := 0.0 }  -- TODO étudiant : linearIBP exo3_after1 (-1.0) 0.0\n",
     "def exo3_output  : Interval := reluIBP exo3_after2\n",
     "\n",
-    "#eval exo3_output  -- solution attendue : { lower := 0.0, upper := 2.5 }"
+    "#eval exo3_output"
    ]
   },
   {
@@ -5283,15 +5179,75 @@
    "id": "t9614ys7bvc",
    "metadata": {
     "papermill": {
-     "duration": 0.010303,
-     "end_time": "2026-06-18T03:11:14.614324+00:00",
+     "duration": 0.039099,
+     "end_time": "2026-10-09T15:38:38.825679+00:00",
      "exception": false,
-     "start_time": "2026-06-18T03:11:14.604021+00:00",
+     "start_time": "2026-10-09T15:38:38.786580+00:00",
      "status": "completed"
     },
     "tags": []
    },
    "source": [
+    "<a id=\"8-conclusion\"></a>\n",
+    "\n",
+    "## 8. Conclusion\n",
+    "\n",
+    "### 8.1 Récapitulatif\n",
+    "\n",
+    "Dans ce notebook, nous avons vu :\n",
+    "\n",
+    "| Concept | Appris | Application |\n",
+    "|---------|--------|-------------|\n",
+    "| **Semantic gap** | Différence PyTorch vs formel | Comprendre les limites de PyTorch |\n",
+    "| **TorchLean** | Architecture 3 modules | Installation et imports |\n",
+    "| **API** | Tenseurs, layers, sequential | Construction de réseaux |\n",
+    "| **Float32** | IEEE-754, arrondi | Preuves d'erreur numérique |\n",
+    "| **IBP** | Propagation d'intervalles | Bornes rapides |\n",
+    "| **CROWN** | Optimisation convexe | Bornes serrées |\n",
+    "| **Applications** | PINNs, Lyapunov | Cas réels |\n",
+    "\n",
+    "### 8.2 Tableau comparatif final\n",
+    "\n",
+    "| Approche | Vérification | Performance | Scalabilité | Garanties |\n",
+    "|----------|---------------|--------------|-------------|-----------|\n",
+    "| **PyTorch** | Tests empiriques | Maximale | Oui | Statistiques seulement |\n",
+    "| **TorchLean IBP** | Formelle | Bonne | Oui | Conservatrices |\n",
+    "| **TorchLean CROWN** | Formelle | Moyenne | Oui | Serrées |\n",
+    "| **SMT solving** | Formelle | Faible | Non | Exactes mais coûteuses |\n",
+    "\n",
+    "### 8.3 Ressources supplémentaires\n",
+    "\n",
+    "**TorchLean** :\n",
+    "- Site officiel : [leandojo.org/torchlean.html](https://leandojo.org/torchlean.html)\n",
+    "- GitHub : [github.com/lean-dojo/TorchLean](https://github.com/lean-dojo/TorchLean)\n",
+    "\n",
+    "**Vérification de réseaux** :\n",
+    "- IBP original : Gowal et al. (2018)\n",
+    "- CROWN : Singh et al. (2019)\n",
+    "- LiRPA : Xu et al. (2020)\n",
+    "\n",
+    "**Lean 4** :\n",
+    "- [Theorem Proving in Lean 4](https://leanprover.github.io/theorem_proving_in_lean4/)\n",
+    "- [Mathematics in Lean](https://leanprover-community.github.io/mathematics_in_lean/)\n",
+    "\n",
+    "### 8.4 Prochains pas\n",
+    "\n",
+    "Après ce notebook, vous pouvez :\n",
+    "\n",
+    "1. **Approfondir TorchLean** : Expérimenter avec des réseaux réels\n",
+    "2. **Lean-12** : Applications avancées de TorchLean (si disponible)\n",
+    "3. **Contribuer** : Au projet TorchLean sur GitHub\n",
+    "4. **Recherche** : Explorer PINNs vérifiés, contrôle formel\n",
+    "\n",
+    "### 8.5 Note sur l'état du projet\n",
+    "\n",
+    "TorchLean est un projet de recherche actif. Certains composants décrits dans ce notebook peuvent être :\n",
+    "- En cours de développement\n",
+    "- Sujets à modifications API\n",
+    "- Partiellement implémentés\n",
+    "\n",
+    "Consultez toujours la documentation officielle pour l'état actuel.\n",
+    "\n",
     "### 8.6 Synthèse visuelle des concepts TorchLean\n",
     "\n",
     "```\n",
@@ -5346,7 +5302,11 @@
     "- **CROWN** : Certificats de haute qualité, analyse fine\n",
     "- **LiRPA** : Support étendu d'activations, recherche\n",
     "\n",
-    "> **Note finale** : TorchLean représente une avancée majeure dans la vérification formelle des réseaux de neurones, comblant le fossé entre l'apprentissage profond et les preuves mathématiques rigoureuses."
+    "> **Note finale** : TorchLean représente une avancée majeure dans la vérification formelle des réseaux de neurones, comblant le fossé entre l'apprentissage profond et les preuves mathématiques rigoureuses.\n",
+    "\n",
+    "***\n",
+    "\n",
+    "**Navigation** : [Index](README.md) | [<< Précédent](Lean-10-LeanDojo.ipynb) | [Version Python](Lean-11b-TorchLean-Python.ipynb) | [Lean-12 Sensitivity >>](Lean-12-Sensitivity-Theorem.ipynb)\n"
    ]
   }
  ],
@@ -5357,24 +5317,24 @@
    "name": "lean4-wsl"
   },
   "language_info": {
-   "codemirror_mode": "python",
+   "codemirror_mode": "lean4",
    "file_extension": ".lean",
    "mimetype": "text/x-lean4",
    "name": "lean4"
   },
   "papermill": {
    "default_parameters": {},
-   "duration": 7.60586,
-   "end_time": "2026-06-18T03:11:14.841429+00:00",
+   "duration": 10.20483,
+   "end_time": "2026-10-09T15:38:39.072697+00:00",
    "environment_variables": {},
    "exception": null,
    "input_path": "Lean-11-TorchLean.ipynb",
-   "output_path": "Lean-11-TorchLean.ipynb",
+   "output_path": "lean11_out.ipynb",
    "parameters": {},
-   "start_time": "2026-06-18T03:11:07.235569+00:00",
+   "start_time": "2026-10-09T15:38:28.867867+00:00",
    "version": "2.7.0"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 5
-}
+}
\ No newline at end of file

From ad1873d1442ed458ac0d593f0e8ae82f7acd2baf Mon Sep 17 00:00:00 2001
From: jsboige <jsboige@gmail.com>
Date: Fri, 9 Oct 2026 20:38:24 +0200
Subject: [PATCH 3/3] Fix(notebooks,#17357): Lean-11 TorchLean -- retirer le
 compteur en prose
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Le garde `prose-counts` refuse un compteur quantitatif sur une ligne
ajoutee (issue #9377). La cellule de conclusion portait
« Architecture 3 modules » ; le compte disparait, le sens est conserve
par les noms de modules, deja cites en section 2.1.

Cellule markdown : aucune reexecution due (C.2).

Co-Authored-By: Claude Haiku 4.5 (1M context) <noreply@anthropic.com>
---
 MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
index 1fb85664a6..6d2bd4c042 100644
--- a/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
+++ b/MyIA.AI.Notebooks/SymbolicAI/Lean/Lean-11-TorchLean.ipynb
@@ -5199,7 +5199,7 @@
     "| Concept | Appris | Application |\n",
     "|---------|--------|-------------|\n",
     "| **Semantic gap** | Différence PyTorch vs formel | Comprendre les limites de PyTorch |\n",
-    "| **TorchLean** | Architecture 3 modules | Installation et imports |\n",
+    "| **TorchLean** | Architecture modulaire (Core, Forum, Verification) | Installation et imports |\n",
     "| **API** | Tenseurs, layers, sequential | Construction de réseaux |\n",
     "| **Float32** | IEEE-754, arrondi | Preuves d'erreur numérique |\n",
     "| **IBP** | Propagation d'intervalles | Bornes rapides |\n",