MacBookPro.lan 2026-4-8:16:58:48

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

@@ -34,7 +34,7 @@
   "allowImageCache": true,
   "allowImageCacheInScene": true,
   "displayExportedImageIfAvailable": false,
-  "previewMatchObsidianTheme": false,
+  "previewMatchObsidianTheme": true,
   "width": "400",
   "height": "",
   "overrideObsidianFontSize": false,
@@ -85,7 +85,7 @@
   "iframelyAllowed": true,
   "pngExportScale": 1,
   "exportWithTheme": true,
-  "exportWithBackground": true,
+  "exportWithBackground": false,
   "exportPaddingSVG": 10,
   "exportEmbedScene": false,
   "keepInSync": true,

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

@@ -5,7 +5,7 @@
     {
       "id": 1,
       "name": "Ma bibliothèque",
-      "lastUpdate": 1775571160432
+      "lastUpdate": 1775656727556
     }
   ],
   "renderCitations": true,

.obsidian/plugins/obsidian-style-settings/data.json

@@ -35,7 +35,7 @@
   "minimal-style@@code-background@@dark": "#1E1E1E",
   "minimal-style@@window-title-off": false,
   "minimal-style@@code-normal@@dark": "#BCBCBC",
-  "minimal-style@@image-muted": 0.7,
+  "minimal-style@@image-muted": 1,
   "minimal-style@@col-alt": false,
   "supercharged-links@@f1e2-3136-color": "#008A88",
   "supercharged-links@@591a-86c0-decoration": "initial",

Excalidraw/demo_théorème_du_début.excalidraw.md

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 ```
 %%

attachments/désintégration audioactive théorème de la fin cycles.excalidraw.md

@@ -0,0 +1,117 @@
+---
+
+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
+## Embedded Files
+04ee9575be008dd3cc75238f0c479af0144df112: $$2\cdot 311322113212221]$$
+
+ed2a4c0fc556d90bae7bdf658819eac067a989bb: $$2\cdot 13211322211312113211]$$
+
+863e0bb6118d1de2696f04a4f43fab8624a7bd64: $$2\cdot 12322211331222113112211]$$
+
+5f0a9eb71a73921b4ed5d95d6d949a915c2fadff: $$2\cdot 1113122113322113111221131221]$$
+
+c3bfc2ab24ffe59ccc732dba128a66901fa6c9e3: $$2\cdot 31221132221222112112322211n]$$
+
+45a03920105d60d417654042595a9400e51e0dff: $$2\cdot 1311222113321132211221121332211n]$$
+
+ca22264e4655342e2d1e39db3f28cc1f519ed819: $$2^2]$$
+
+62670f424a7fd99dd2c0a9e49105a9007e1610c8: $$(1)$$
+
+acd3990fdc2fa19b40c17d95a96c473a5d002d33: $$(2)$$
+
+2e1dd3e45c3cd8ecb31469cdc166428d1a0b5d8a: $$(3)$$
+
+%%
+## Drawing
+```compressed-json
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+```
+%%

désintégration audioactive.md

@@ -22,7 +22,8 @@ header-auto-numbering:
 
 # Notations
  - On assimilera toujours les éléments d'un terme à des chiffres
- - On pourra noter $,12,23,11,$ : les virgules précisent le parsing
+ - On pourra noter $,12,23,11,$ : les virgules précisent le "parsing", c'est-à-dire la bonne manière de lire la chaîne
+     - = $\dots 233 \dots \longrightarrow \dots ,12,23, \dots$ mais $122111 \centernot{\longrightarrow} \dots ,12,23,1\dots$  même si $122111 \longrightarrow \dots 12231 \dots$
  - $L \longrightarrow L'$ signifie que $L$ est dérivée en $L'$ par désintégration audioactive
      - On note aussi $L \longrightarrow L' \longrightarrow L'' \longrightarrow \cdots$ pour $L \longrightarrow L'$ et $L' \longrightarrow L''$ et $L'' \longrightarrow \cdots$
  - $L_{n}$ est le $n^{\text{ème}}$ *descendant* de $L$ (le résultat de $n$ dérivations de $L$)
@@ -36,6 +37,7 @@ header-auto-numbering:
  - $X$ désigne un chiffre arbitraire (non nul)
      - = $X^{0}a^{\alpha}b^{\beta}c^{\gamma}$ correspond à $[a^{\alpha}b^{\beta}c^{\gamma}$
      - = $a^{\alpha}b^{\beta}c^{\gamma}X^{0}$ correspond à $a^{\alpha}b^{\beta}c^{\gamma}]$
+     - = 
  - $\neq n$ désigne n'importe quel chiffre (éventuellement 0) autre que $n$
      - = $a^{\alpha}b^{\beta}c^{\gamma}X^{\neq 0}$ signifie $a^{\alpha}b^{\beta}c^{\gamma}$ suivi d'au moins un autre chiffre
      - = $a^{\alpha}b^{\beta}c^{\gamma} (\neq 2)^{\neq 0}$ signifie que ce dernier chiffre n'est pas un $2$
@@ -65,11 +67,9 @@ header-auto-numbering:
 
 > [!definition] Atome
 > Les **atomes** (ou *éléments*) sont les chaînes qui ne possèdent pas de découpage non trivial.
-> - source:: [[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=181&selection=221,11,241,7&color=note|(John Horton Conway, 1987)]]
 ^def-atome
 
  - i toute chaîne est **composée** d'un certain nombre d'éléments. On dit que cette chaîne **comprends** lesdits éléments.
-     - source:: [[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=181&selection=243,5,260,9&color=note|(John Horton Conway, 1987)]]
 
 
 ## Théorèmes
@@ -203,7 +203,7 @@ header-auto-numbering:
 > >  - $[n^{1}$
 > > 
 > > De là, on observe que toutes les possibilités convergent vers l'un des cycles donnés :
-> > ![[demo_théorème_du_début.excalidraw]]
+> > ![[demo_théorème_du_début.excalidraw|700]]
 > > 
 > > Par ailleurs, si $R$ commence par $[22$ :
 > >  - si $R = [22]$ la preuve est trivialle
@@ -235,7 +235,7 @@ header-auto-numbering:
 > >  - $[n^{1}$
 > > 
 > > Cela nous permet d'atteindre le schéma original de Conway :
-> > ![[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=186&rect=12,345,377,408|schéma original de Conway p.186]]
+> > ![[sources/1 - articles/Open problems in communication and computation (Cover, T. M., 1938-, Gopinath, B) (z-library.sk, 1lib.sk, z-lib.sk).pdf#page=186&rect=12,345,377,408&width=800|schéma original de Conway p.186]]
 ^theoreme-debut
 
 > [!proposition]+ théorème du découpage
@@ -254,7 +254,15 @@ header-auto-numbering:
 
 > [!proposition]+ Théorème de la fin
 > La fin d'une chaîne finit toujours par atteindre l'un de ces cycles :
+> ![[attachments/désintégration audioactive théorème de la fin cycles.excalidraw|950]]
 > 
+> > [!démonstration]+ Démonstration
+> >  - Une chaîne se terminant par $1$ apparaîtra nécessairement dans cette chaîne de dérivations (en effet, tous les cas de chaîne finissant par $1$ y sont présents) :
+> >    $1^{\geq 3}] \longrightarrow \underbrace{(\neq 2)^{X}1^{1}]}_{\substack{\text{plus général}\\\text{que }(\geq 3)^{X}1^{1}]}} \longrightarrow (\neq 2)^{X}1^{2}] \longrightarrow (\neq 2)^{X}2^{1}1^{1}] \longrightarrow \underbrace{2^{X\neq 2}1^{2}]}_{\substack{\text{fin de}\\(\neq 2)^{X}1^{1}2^{1}1^{2}]}} \longrightarrow 2^{2}1^{1}] \longrightarrow 2^{2}1^{2}] \longrightarrow 2^{3}1^{1}]$
+> >    Ce qui montre que toute chaîne se terminant par $1$ finit par atteindre une chaîne se terminant par $2^{3}1^{1}]$.
+> >    De là, en dérivant cette fin plusieurs fois, on obtient successivement :
+> >      - 
+> >  -