device-52.home 2026-3-21:19:6:3

.obsidian/community-plugins.json

@@ -42,5 +42,6 @@
   "obsidian-kanban",
   "obsidian-pandoc",
   "obsidian-enhancing-export",
-  "heatmap-tracker"
+  "contribution-graph",
+  "header-enhancer"
 ]

.obsidian/plugins/auto-template-trigger/data.json

@@ -3,6 +3,10 @@
     {
       "folderPath": "/",
       "templateName": "default new note"
+    },
+    {
+      "folderPath": "daily",
+      "templateName": "daily note"
     }
   ],
   "disablePrompt": false,

.obsidian/plugins/breadcrumbs/data.json

@@ -631,7 +631,7 @@
           "prevs"
         ],
         "lock_view": false,
-        "lock_path": "daily/2026-03-21.md"
+        "lock_path": "suites finies d'entiers comme fonctions récursives primitives.md"
       },
       "tree": {
         "collapse": false,
@@ -651,7 +651,7 @@
           "alias": false
         },
         "lock_view": false,
-        "lock_path": ""
+        "lock_path": "suites finies d'entiers comme fonctions récursives primitives.md"
       }
     },
     "codeblocks": {

.obsidian/plugins/header-enhancer/data.json

@@ -0,0 +1,26 @@
+{
+  "language": "en",
+  "showOnStatusBar": true,
+  "showOnSidebar": true,
+  "isAutoDetectHeaderLevel": false,
+  "startHeaderLevel": 1,
+  "endHeaderLevel": 6,
+  "autoNumberingMode": "on",
+  "autoNumberingStartNumber": "1",
+  "autoNumberingSeparator": ".",
+  "autoNumberingHeaderSeparator": "\t",
+  "updateBacklinks": false,
+  "yamlFallbackMode": "use_default",
+  "yamlDefaultStartLevel": 2,
+  "yamlDefaultEndLevel": 6,
+  "yamlDefaultStartNumber": "1",
+  "yamlDefaultSeparator": ".",
+  "globalAutoNumberingEnabled": true,
+  "perDocumentStates": "{\"suite finies d'entiers.md\":false}",
+  "isSeparateHeaderFont": false,
+  "headerFontFamily": "inherit",
+  "headerFontSize": "inherit",
+  "isSeparateTitleFont": false,
+  "titleFontFamily": "inherit",
+  "titleFontSize": "inherit"
+}

.obsidian/plugins/header-enhancer/manifest.json

@@ -0,0 +1,11 @@
+{
+	"id": "header-enhancer",
+	"name": "Header Enhancer",
+	"version": "0.5.1",
+	"minAppVersion": "0.14.0",
+	"description": "Level up your headers, customize your notes. Header Enhancer makes your notes header better and more useful.",
+	"author": "Hobee Liu",
+	"authorUrl": "https://github.com/HoBeedzc",
+	"fundingUrl": "https://bmc.link/hobee",
+	"isDesktopOnly": false
+}

.obsidian/plugins/header-enhancer/styles.css

@@ -0,0 +1,8 @@
+/*
+
+This CSS file will be included with your plugin, and
+available in the app when your plugin is enabled.
+
+If your plugin does not need CSS, delete this file.
+
+*/

.obsidian/plugins/heatmap-tracker/manifest.json

@@ -1,12 +0,0 @@
-{
-	"id": "heatmap-tracker",
-	"name": "Heatmap Tracker",
-	"version": "2.1.7",
-	"minAppVersion": "0.1.0",
-	"description": "Visualize your activity and track goals, progress, habits, tasks, exercise, finances, and more—all in a single, interactive heatmap!",
-	"author": "Maksim Rubanau",
-	"isDesktopOnly": false,
-	"fundingUrl": {
-		"Buy Me a Coffee": "https://www.buymeacoffee.com/mrubanau"
-	}
-}

.obsidian/plugins/obsidian-excalidraw-plugin/data.json

@@ -113,7 +113,7 @@
   "library2": {
     "type": "excalidrawlib",
     "version": 2,
-    "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.20.2",
+    "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/2.21.2",
     "libraryItems": []
   },
   "imageElementNotice": true,

.obsidian/plugins/obsidian-pandoc-reference-list/data.json

@@ -5,7 +5,7 @@
     {
       "id": 1,
       "name": "Ma bibliothèque",
-      "lastUpdate": 1774111558215
+      "lastUpdate": 1774114564025
     }
   ],
   "renderCitations": true,

.obsidian/types.json

@@ -95,6 +95,7 @@
     "lt-disabledCategories": "multitext",
     "excalidraw-export-internal-links": "checkbox",
     "date-rendu": "date",
-    "TQ_show_toolbar": "checkbox"
+    "TQ_show_toolbar": "checkbox",
+    "sport": "checkbox"
   }
 }

S2 LOGOS . incomplétude et indécidabilité.md

@@ -9,4 +9,10 @@ date-rendu:
   - 2026-03-26
 type-rendu:
   - partiel
+BC-list-note-field: down
 ---
+
+- [[fonction récursive primitive]]
+    - [[schéma mu borné|schéma µ borné]]
+    - [[suites finies d'entiers comme fonctions récursives primitives]]
+- [[ensemble récursif primitif]]

S2 LOGOS.md

@@ -12,7 +12,7 @@ type: tree
 collapse: false
 show-attributes: [field]
 field-groups: [downs]
-depth: [0, 0]
+depth: [0, 1]
 ```
 
 

attachments/ordre sur les couples d'entiers 2026-03-21 18.43.49.excalidraw.md

@@ -0,0 +1,186 @@
+---
+
+excalidraw-plugin: parsed
+tags: [excalidraw]
+
+---
+==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
+
+
+# Excalidraw Data
+
+## Text Elements
+(0, 0) ^JA63goKG
+
+(0, 0) ^6tqLjjL9
+
+(0, 0) ^qDjoBHEx
+
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+
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+
+%%
+## Drawing
+```compressed-json
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+
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+
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+```
+%%

daily/2026-03-20.md

@@ -0,0 +1,23 @@
+---
+sport: true
+---
+
+# Todo
+
+```tasks
+due 2026-03-20
+not done
+```
+# I did
+
+> [!smallquery]- Modified files
+> ```dataview
+> LIST file.mtime
+> where file.mtime > date(this.file.name) and file.mtime < (date(this.file.name) + dur(1 day)) sort file.mtime asc
+> ```
+```tasks
+done 2026-03-20
+short mode
+```
+# I am gratefull to
+

daily/2026-03-21.md

@@ -1,3 +1,7 @@
+---
+sport: "true"
+---
+
 # Todo
 
 ```tasks
@@ -5,6 +9,7 @@ due 2026-03-21
 not done
 ```
 # I did
+- [ ] #task test
 
 > [!smallquery]- Modified files
 > ```dataview
@@ -17,3 +22,5 @@ short mode
 ```
 # I am gratefull to
 
+
+

daily/2026-03-22.md

@@ -0,0 +1,23 @@
+---
+sport: true
+---
+
+# Todo
+
+```tasks
+due 2026-03-22
+not done
+```
+# I did
+
+> [!smallquery]- Modified files
+> ```dataview
+> LIST file.mtime
+> where file.mtime > date(this.file.name) and file.mtime < (date(this.file.name) + dur(1 day)) sort file.mtime asc
+> ```
+```tasks
+done 2026-03-22
+short mode
+```
+# I am gratefull to
+

flashcards politique et sociologie.md

@@ -6,7 +6,7 @@ salaire (net mensuel) **médian** en france :: 1 850€/mois
 <!--SR:!2024-10-18,284,250-->
 
 salaire (net mensuel) **médian** en france **pour un couple** :: 3 857€/mois
-<!--SR:!2024-09-04,16,150-->
+<!--SR:!2026-03-21,1,130-->
 
 pourcentage de fils/filles d'ouvriers qui **sortent** de l'université dans des filières d'excellence :: 3%
 <!--SR:!2027-08-31,1107,310-->

fonction pi.md

@@ -22,18 +22,3 @@ aliases:
 > > $\pi(n+1) = \mu p \leq (n+1)! \quad \left(\mathrm{sg}(p \dot{-}\pi( n)) \cdot \left( 1\dot{-} \mathrm{sg} \left( \sum\limits_{d=1}^{d=p}d|p \right)  \right) \right)$
 ^recursive-primitive
 # Exemples
-
-```heatmap-tracker
-heatmapTitle: Test
-heatmapSubtitle: ""
-property: nb_times_seen
-year: 2025
-separateMonths: true
-showCurrentDayBorder: true
-disableFileCreation: false
-excludeFalsy: false
-colorScheme:
-  paletteName: default
-ui: {}
-```
-

fonction récursive primitive.md

@@ -183,6 +183,7 @@ Dans cette section, on démontre que quelques fonctions élémentaires sont réc
 > > $\chi _{B}(\overline{x}, z) = \mathrm{sg}\left( \sum\limits_{t=0}^{z} \chi _{A}(\overline{x}, t) \right)$
 > > et celle de $C$ par :
 > > $\chi _{C}(\overline{x}, z) = \mathrm{sg}\left( \prod\limits_{t=0}^{z} \chi _{A}(\overline{x}, t) \right)$
+^cloture-par-quantification-bornee
 
 ## Schémas de définition supplémentaires
 On peut trouver de nouveaux schémas de définitions de fonctions qui sont stables sur les fonctions récursives primitives.

suite finies d'entiers.md

@@ -18,18 +18,7 @@ aliases:
 
 > [!proposition]+ Représentation des suites comme nombres
 > On peut trouver une [[bijection]] entre $\mathbb{N}$ et l'ensemble des suites finies à $p$ éléments.
-> De plus, cette bijection est [[fonction récursive primitive|récursive primitive]].
+> De plus, cette bijection peut être [[fonction récursive primitive|récursive primitive]].
-> > [!démonstration]+ Démonstration
-> > On procède en définissant l'application de $\mathscr{S} \to \mathbb{N}$ suivante :
-> > $\Omega((x_0, x_1, \dots, x_{p})) = \pi(0)^{x_0} \cdot \pi(1)^{x_1} \cdot\cdots \cdot \pi(p)^{x_{p}}$ (voir [[fonction pi|fonction π]])
-> > On sait par l'arithmétique ([[décomposition en facteurs premiers]]) que cette fonction est bien une bijection.
-> > Par ailleurs, comme [[fonction pi#^recursive-primitive|la fonction π est récursive primitive]], on sait que $\Omega$ est récursive primitive aussi
-> > Montrons maintenant que la réciproque de $\Omega$ est également récursive primitive :
-> > définissons la fonction $\delta \in \mathscr{F}_{2}$ :
-> > $\delta(i, x) := \mu z \leq x \quad (x \text{ n'est pas divisible par } \pi(i)^{z+1})$
-> > On sait que [[divisibilité#^recursive-primitive|le prédicat de divisibilité est récursif primitif]], ce qui montre que $\delta$ est récursive primitive.
-> > Maintenant, la fonction $\lambda x. (\delta(1, x), \delta(2, x), \dots, \delta(p, x))$ est bien la réciproque de $\Omega$
-> > une ligne super long avec plein de text super long qui va dépasser jusqu'à la fin de la ligne pour pouvoir tester si le symbole bave et 
 
 # Exemples
 

suites finies d'entiers comme fonctions récursives primitives.md

@@ -0,0 +1,40 @@
+---
+up:
+  - "[[suite finies d'entiers]]"
+  - "[[fonction récursive primitive]]"
+tags:
+  - s/maths/logique
+  - s/informatique
+aliases:
+---
+
+
+> [!proposition]+ Représentation avec des couples
+> Le but est de trouver une fonction qui fasse l'association entre un nombre et un $p$-uplet (une suite de $p$ entiers).
+> On veut montrer qu'il existe $\alpha _{p} \in \mathscr{F}_{p}$ et $\beta _{p}^{1}, \beta _{p}^{2}, \dots, \beta _{p}^{p} \in \mathscr{F}_{p}$ telles que $\alpha _{p}$ est une [[bijection]] et que l'application réciproque de $\alpha _{p}$ soit $\lambda x. (\beta _{p}^{1}, \beta _{p}^{2}, \dots, \beta _{p}^{p})$
+>  - **Couples :**
+>    On commence par construire $\alpha _{2}$ pour les couples, dont la réciproque doit être $\lambda x. (\beta _{2}^{1}, \beta _{2}^{2})$ :
+>    Pour cela, on décide d'ordonner les couples d'entiers comme suit :
+>    ![[attachments/ordre sur les couples d'entiers 2026-03-21 18.43.49.excalidraw]]
+>    C'est-à-dire en suivant les diagonales à $x+y$ constant, en commençant par $x+y=0$, puis $x+y=1$ ...
+>    la valeur de $\alpha_2(x, y)$ sera alors le nombre de couples précédant $(x, y)$ dans cette énumération
+>    tes
+>    Considérons le couple $(p, n)$ :
+>    Il se trouve dans la diagonale $p+n$. Les couples avant cette diagonale sont au nombre de $\frac{(p+n)(p+n+1)}{2}$, et le couple $(p, n)$ est le $n^{\text{ème}}$ de sa diagonale.
+>    Cela montre que $\alpha _{2}(p, n) = \frac{1}{2}(p+n)(p+n+1)+n$.
+>    On peut ensuite retrouver $\beta _{2}^{1}$ et $\beta _{2}^{2}$ comme suit (à l'aide de [[schéma mu borné|schémas µ bornés]] et de la [[fonction récursive primitive#^cloture-par-quantification-bornee|clôture par quantification bornée]]) :
+>      - $\beta _{2}^{1} = \mu z \leq x \quad (\exists w\leq x,\quad \alpha_2(z, w) = x)$
+>      - $\beta _{2}^{2} = \mu z \leq x \quad (\exists w\leq x,\quad \alpha_2(w, z) = x)$
+
+
+> [!proposition]+ Seconde approche
+> On procède en définissant l'application de $\mathscr{S} \to \mathbb{N}$ suivante :
+> $\Omega((x_0, x_1, \dots, x_{p})) = \pi(0)^{x_0} \cdot \pi(1)^{x_1} \cdot\cdots \cdot \pi(p)^{x_{p}}$ (voir [[fonction pi|fonction π]])
+> On profite ici de la [[décomposition en facteurs premiers]].
+> Par ailleurs, comme [[fonction pi#^recursive-primitive|la fonction π est récursive primitive]], on sait que $\Omega$ est récursive primitive aussi
+> Montrons maintenant que la réciproque de $\Omega$ est également récursive primitive :
+> définissons la fonction $\delta \in \mathscr{F}_{2}$ :
+> $\delta(i, x) := \mu z \leq x \quad (x \text{ n'est pas divisible par } \pi(i)^{z+1})$
+> On sait que [[divisibilité#^recursive-primitive|le prédicat de divisibilité est récursif primitif]], ce qui montre que $\delta$ est récursive primitive.
+> La fonction $\lambda x. (\delta(1, x), \delta(2, x), \dots, \delta(p, x))$ est bien la réciproque de $\Omega$
+>  - i Cette approche est moins parfaite car $\Omega$ n'est pas bijective

things to do.md

@@ -4,6 +4,34 @@
 > short mode
 > ```
 
+```contributionGraph
+title: Tasks completed
+graphType: default
+dateRangeValue: 180
+dateRangeType: LATEST_DAYS
+startOfWeek: 0
+showCellRuleIndicators: true
+titleStyle:
+  textAlign: left
+  fontSize: 15px
+  fontWeight: normal
+dataSource:
+  type: ALL_TASK
+  value: ""
+  dateField:
+    type: FILE_NAME
+  filters:
+    - id: "1774113825001"
+      type: CONTAINS_ANY_TAG
+      value:
+        - "#task"
+    - id: "1774114013540"
+      type: STATUS_IS
+      value: COMPLETED
+fillTheScreen: false
+enableMainContainerShadow: false
+cellStyleRules: []
+```
 
 > [!smallquery] Done
 > ```tasks