MacBook-Pro-de-Oscar.local 2026-6-11:0:35:19

.obsidian/appearance.json

@@ -1,7 +1,7 @@
 {
   "theme": "system",
   "cssTheme": "Minimal",
-  "baseFontSize": 22,
+  "baseFontSize": 28,
   "enabledCssSnippets": [
     "pdf_darkmode",
     "query_header_title",

.obsidian/community-plugins.json

@@ -26,7 +26,6 @@
   "pdf-plus",
   "breadcrumbs",
   "obsidian-day-planner",
-  "obsidian-advanced-slides",
   "calendar",
   "obsidian-completr",
   "dataview",
@@ -41,5 +40,6 @@
   "notebook-navigator",
   "obsidian-pandoc",
   "break-page",
-  "obsidian-list-callouts"
+  "obsidian-list-callouts",
+  "math-in-callout"
 ]

.obsidian/graph.json

@@ -130,6 +130,6 @@
   "repelStrength": 5.263671875,
   "linkStrength": 1,
   "linkDistance": 30,
-  "scale": 0.1345612381098431,
+  "scale": 0.31211118817502304,
   "close": true
 }

.obsidian/plugins/better-export-pdf/data.json

@@ -0,0 +1,30 @@
+{
+  "showTitle": false,
+  "maxLevel": "6",
+  "displayHeader": true,
+  "displayFooter": true,
+  "headerTemplate": "<div style=\"padding-left: 2cm; padding-right: 2cm; width: 100%; display: flex; justify-content: space-between; font-size:10px;\"><span class=\"title\"></span><span>Oscar Plaisant</span></div>",
+  "footerTemplate": "<div style=\"width: 100vw;font-size:10px;text-align:center;\"><span class=\"pageNumber\"></span> / <span class=\"totalPages\"></span></div>",
+  "printBackground": false,
+  "generateTaggedPDF": false,
+  "displayMetadata": true,
+  "debug": false,
+  "isTimestamp": false,
+  "enabledCss": false,
+  "concurrency": "5",
+  "prevConfig": {
+    "pageSize": "A4",
+    "marginType": "1",
+    "showTitle": false,
+    "open": true,
+    "scale": 59,
+    "landscape": false,
+    "marginTop": "5",
+    "marginBottom": "5",
+    "marginLeft": "20",
+    "marginRight": "20",
+    "displayHeader": true,
+    "displayFooter": true,
+    "cssSnippet": "0"
+  }
+}

.obsidian/plugins/better-export-pdf/manifest.json

@@ -0,0 +1,11 @@
+{
+  "id": "better-export-pdf",
+  "name": "Better Export PDF",
+  "version": "1.11.0",
+  "minAppVersion": "0.15.0",
+  "description": "Export your notes to PDF, support export preview, add bookmarks outline and header/footer.",
+  "author": "l1xnan",
+  "authorUrl": "https://github.com/l1xnan",
+  "fundingUrl": "https://www.buymeacoffee.com/l1xnan",
+  "isDesktopOnly": true
+}

.obsidian/plugins/better-export-pdf/styles.css

@@ -0,0 +1,67 @@
+#better-export-pdf {
+  display: flex;
+  flex-direction: row;
+  height: 75vh;
+}
+
+#better-export-pdf .pdf-preview {
+  flex: auto;
+  position: relative;
+  display: flex;
+  flex-direction: column;
+  overflow-x: hidden;
+  overflow-y: scroll;
+  align-content: flex-start;
+}
+
+#better-export-pdf .pdf-preview .webview-wrapper {
+  position: relative;
+  height: 100%;
+  width: 100%;
+}
+
+#better-export-pdf .pdf-preview .print-size {
+  position: absolute;
+  right: 8px;
+  top: 8px;
+  z-index: 99;
+  font-size: 0.6rem;
+  white-space: pre-wrap;
+  text-align: right;
+  visibility: hidden;
+}
+
+#better-export-pdf .pdf-preview > div {
+  flex: 1;
+  height: 100%;
+  width: 100%;
+}
+#better-export-pdf .pdf-preview > div.progress {
+  flex: none;
+  height: auto;
+  width: 100%;
+  text-align: left;
+}
+
+#better-export-pdf .pdf-preview .filename {
+  font-size: 0.75rem;
+  color: var(--color-base-60);
+}
+#better-export-pdf .pdf-preview .filename:not(:first-child) {
+  padding-top: calc(var(--p-spacing));
+}
+
+#better-export-pdf webview {
+  flex: 1;
+  height: 100%;
+  width: 100%;
+}
+
+#better-export-pdf .setting-wrapper {
+  width: 320px;
+  margin-left: 16px;
+}
+
+#better-export-pdf .setting-wrapper .setting-item[hidden] {
+  display: none;
+}

.obsidian/plugins/breadcrumbs/data.json

@@ -27,6 +27,9 @@
     },
     {
       "label": "part"
+    },
+    {
+      "label": "sibling"
     }
   ],
   "edge_field_groups": [
@@ -49,7 +52,8 @@
     {
       "label": "sames",
       "fields": [
-        "same"
+        "same",
+        "sibling"
       ]
     },
     {
@@ -152,7 +156,8 @@
       "default_neighbour_field": ""
     },
     "tag_note": {
-      "default_field": "up"
+      "default_field": "up",
+      "default_sibling_field": ""
     },
     "regex_note": {
       "default_field": "up"
@@ -161,18 +166,52 @@
       "enabled": false,
       "delimiter": ".",
       "default_field": "up",
-      "display_trimmed": false
+      "display_trimmed": false,
+      "default_sibling_field": ""
     },
     "johnny_decimal_note": {
       "enabled": false,
       "delimiter": ".",
-      "default_field": "up"
+      "default_field": "up",
+      "default_sibling_field": ""
     },
     "date_note": {
       "enabled": false,
       "date_format": "yyyy-MM-dd",
       "default_field": "next",
-      "stretch_to_existing": false
+      "stretch_to_existing": false,
+      "week_start": "monday",
+      "week": {
+        "enabled": false,
+        "date_format": "kkkk-'W'WW",
+        "folder": "",
+        "next_field": "next",
+        "up_field": "up"
+      },
+      "month": {
+        "enabled": false,
+        "date_format": "yyyy-MM",
+        "folder": "",
+        "next_field": "next",
+        "up_field": "up"
+      },
+      "quarter": {
+        "enabled": false,
+        "date_format": "yyyy-'Q'q",
+        "folder": "",
+        "next_field": "next",
+        "up_field": "up"
+      },
+      "year": {
+        "enabled": false,
+        "date_format": "yyyy",
+        "folder": "",
+        "next_field": "next",
+        "up_field": "up"
+      }
+    },
+    "traverse_note": {
+      "default_field": "up"
     }
   },
   "views": {
@@ -188,7 +227,7 @@
         "default_depth": 999,
         "no_path_message": "",
         "show_controls": false,
-        "merge_fields": false,
+        "merge_fields": true,
         "field_group_labels": [
           "ups"
         ],
@@ -210,8 +249,15 @@
             "prevs"
           ],
           "next": [
-            "nexts"
+            "nexts",
+            "sames"
           ]
+        },
+        "period_rows": {
+          "week": false,
+          "month": false,
+          "quarter": false,
+          "year": false
         }
       }
     },
@@ -240,7 +286,7 @@
           "prevs"
         ],
         "lock_view": false,
-        "lock_path": "désintégration audioactive.md",
+        "lock_path": "anneau.md",
         "custom_sort_fields": false,
         "custom_sort_field_labels": []
       },
@@ -249,8 +295,9 @@
         "show_attributes": [],
         "merge_fields": false,
         "lock_view": false,
-        "lock_path": "désintégration audioactive.md",
+        "lock_path": "anneau intègre.md",
         "field_group_labels": [
+          "ups",
           "downs"
         ],
         "edge_sort_id": {
@@ -261,7 +308,12 @@
           "ext": false,
           "folder": false,
           "alias": false
-        }
+        },
+        "default_depth": 5,
+        "find_root": true,
+        "find_root_field_group_labels": [
+          "ups"
+        ]
       }
     },
     "codeblocks": {
@@ -322,5 +374,12 @@
   },
   "debug": {
     "level": "INFO"
+  },
+  "self_is_sibling": [
+    "same"
+  ],
+  "_bc_migrations": {
+    "tree_ups_with_downs_default": true,
+    "tree_find_root_default": true
   }
 }

.obsidian/plugins/breadcrumbs/manifest.json

@@ -1,12 +1,15 @@
 {
 	"id": "breadcrumbs",
 	"name": "Breadcrumbs",
-	"version": "4.5.0",
-	"minAppVersion": "1.0.0",
-	"description": "Add structured hierarchies to your notes",
-	"author": "SkepticMystic",
-	"authorUrl": "https://github.com/SkepticMystic/breadcrumbs",
-	"fundingUrl": "https://github.com/SkepticMystic/breadcrumbs#donations",
-	"helpUrl": "https://publish.obsidian.md/breadcrumbs-docs",
+	"version": "4.14.2",
+	"minAppVersion": "1.12.3",
+	"description": "Add structured hierarchies to your notes.",
+	"author": "MichaelPPorter",
+	"authorUrl": "https://github.com/michaelpporter",
+	"fundingUrl": {
+		"GitHub Sponsors": "https://github.com/sponsors/michaelpporter",
+		"Buy Me a Coffee": "https://www.buymeacoffee.com/michaelpporter"
+	},
+	"helpUrl": "https://breadcrumbs-docs.michaelpporter.com",
 	"isDesktopOnly": false
-}
+}

.obsidian/plugins/breadcrumbs/styles.css

@@ -1 +1,2 @@
-.container{width:100%}@media (min-width:640px){.container{max-width:640px}}@media (min-width:768px){.container{max-width:768px}}@media (min-width:1024px){.container{max-width:1024px}}@media (min-width:1280px){.container{max-width:1280px}}@media (min-width:1536px){.container{max-width:1536px}}.\!collapse{visibility:collapse!important}.collapse{visibility:collapse}.absolute{position:absolute}.relative{position:relative}.sticky{position:sticky}.bottom-2{bottom:.5rem}.left-2{left:.5rem}.right-2{right:.5rem}.top-2{top:.5rem}.mx-auto{margin-left:auto;margin-right:auto}.my-0{margin-top:0;margin-bottom:0}.my-2{margin-top:.5rem;margin-bottom:.5rem}.mb-1{margin-bottom:.25rem}.mb-4{margin-bottom:1rem}.block{display:block}.flex{display:flex}.grid{display:grid}.contents{display:contents}.hidden{display:none}.aspect-square{aspect-ratio:1/1}.h-32{height:8rem}.w-10{width:2.5rem}.w-48{width:12rem}.w-60{width:15rem}.w-8{width:2rem}.w-full{width:100%}.shrink{flex-shrink:1}.grow{flex-grow:1}.transform{transform:translate(var(--tw-translate-x),var(--tw-translate-y)) rotate(var(--tw-rotate)) skewX(var(--tw-skew-x)) skewY(var(--tw-skew-y)) scaleX(var(--tw-scale-x)) scaleY(var(--tw-scale-y))}.cursor-pointer{cursor:pointer}.scroll-mt-40{scroll-margin-top:10rem}.flex-col{flex-direction:column}.flex-wrap{flex-wrap:wrap}.items-center{align-items:center}.justify-center{justify-content:center}.justify-between{justify-content:space-between}.gap-0\.5{gap:.125rem}.gap-1{gap:.25rem}.gap-1\.5{gap:.375rem}.gap-2{gap:.5rem}.gap-3{gap:.75rem}.gap-4{gap:1rem}.gap-7{gap:1.75rem}.border{border-width:1px}.p-1{padding:.25rem}.p-2{padding:.5rem}.px-3{padding-left:.75rem;padding-right:.75rem}.px-4{padding-left:1rem;padding-right:1rem}.py-2{padding-top:.5rem;padding-bottom:.5rem}.pl-2{padding-left:.5rem}.pl-4{padding-left:1rem}.pr-10{padding-right:2.5rem}.pr-2{padding-right:.5rem}.text-left{text-align:left}.text-right{text-align:right}.font-mono{font-family:ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,Liberation Mono,Courier New,monospace}.text-lg{font-size:1.125rem;line-height:1.75rem}.text-xl{font-size:1.25rem;line-height:1.75rem}.font-semibold{font-weight:600}.filter{filter:var(--tw-blur) var(--tw-brightness) var(--tw-contrast) var(--tw-grayscale) var(--tw-hue-rotate) var(--tw-invert) var(--tw-saturate) var(--tw-sepia) var(--tw-drop-shadow)}.BC-matrix-view hr:last-child{display:none}.BC-page-views.BC-page-views-sticky{z-index:50;position:sticky;top:calc(var(--file-margins)*-1);background-color:var(--background-primary)}.text-faint{color:var(--text-faint)}.text-warning{color:var(--text-warning)}.text-error{color:var(--text-error)}
+/*! tailwindcss v4.3.0 | MIT License | https://tailwindcss.com */
+@layer properties{@supports (((-webkit-hyphens:none)) and (not (margin-trim:inline))) or ((-moz-orient:inline) and (not (color:rgb(from red r g b)))){*,:before,:after,::backdrop{--tw-border-style:solid;--tw-blur:initial;--tw-brightness:initial;--tw-contrast:initial;--tw-grayscale:initial;--tw-hue-rotate:initial;--tw-invert:initial;--tw-opacity:initial;--tw-saturate:initial;--tw-sepia:initial;--tw-drop-shadow:initial;--tw-drop-shadow-color:initial;--tw-drop-shadow-alpha:100%;--tw-drop-shadow-size:initial}}}.collapse{visibility:collapse}.invisible{visibility:hidden}.visible{visibility:visible}.absolute{position:absolute}.fixed{position:fixed}.relative{position:relative}.static{position:static}.sticky{position:sticky}.container{width:100%}.mx-auto{margin-inline:auto}.block{display:block}.contents{display:contents}.flex{display:flex}.grid{display:grid}.hidden{display:none}.inline{display:inline}.list-item{display:list-item}.table{display:table}.aspect-square{aspect-ratio:1}.w-full{width:100%}.flex-1{flex:1}.shrink{flex-shrink:1}.grow{flex-grow:1}.cursor-pointer{cursor:pointer}.flex-col{flex-direction:column}.flex-wrap{flex-wrap:wrap}.items-center{align-items:center}.justify-between{justify-content:space-between}.justify-center{justify-content:center}.border{border-style:var(--tw-border-style);border-width:1px}.text-left{text-align:left}.text-right{text-align:right}.lowercase{text-transform:lowercase}.uppercase{text-transform:uppercase}.opacity-20{opacity:.2}.opacity-60{opacity:.6}.filter{filter:var(--tw-blur,) var(--tw-brightness,) var(--tw-contrast,) var(--tw-grayscale,) var(--tw-hue-rotate,) var(--tw-invert,) var(--tw-saturate,) var(--tw-sepia,) var(--tw-drop-shadow,)}.BC-matrix-view hr:last-child{display:none}.BC-page-views{pointer-events:none}.BC-page-views *{pointer-events:auto}.BC-page-views.BC-page-views-sticky{z-index:50;top:calc(var(--file-margins) * -1);background-color:var(--background-primary);position:sticky}.cm-scroller.BC-cm-scroller-inline-page-views:not(.banner-view-active){flex-wrap:wrap;align-content:flex-start}.cm-scroller.BC-cm-scroller-inline-page-views>.BC-page-views{box-sizing:border-box;flex:none;align-self:stretch;width:100%;max-width:100%}.cm-scroller.BC-cm-scroller-inline-page-views.banner-view-active>.cm-gutters{display:none}:root .cm-scroller.BC-cm-scroller-inline-page-views.banner-view-active>.banner-wrapper{width:100%;max-width:100%;margin-left:0;margin-right:0}:root .cm-scroller.BC-cm-scroller-inline-page-views.banner-view-active>.cm-sizer{width:100%;max-width:100%;margin-left:auto;margin-right:auto}.cm-scroller.BC-cm-scroller-inline-page-views>.banner-image{pointer-events:none;position:absolute}.markdown-source-view>.BC-page-views{width:100%;max-width:100%}.markdown-source-view.is-readable-line-width>.BC-page-views,.markdown-source-view.is-readable-line-width .BC-page-views-inner{max-width:var(--file-line-width);margin-left:auto;margin-right:auto}.markdown-source-view:not(.is-readable-line-width)>.BC-page-views.BC-page-views-sticky{max-width:700px;margin-left:auto;margin-right:auto}.markdown-source-view.is-readable-line-width .cm-scroller.BC-cm-scroller-inline-page-views.banner-view-active>.cm-sizer{max-width:700px}.markdown-source-view.is-readable-line-width .cm-scroller.BC-cm-scroller-inline-page-views.banner-view-active>.BC-page-views{max-width:700px;margin-left:auto;margin-right:auto}.text-faint{color:var(--text-faint)}.text-warning{color:var(--text-warning)}.text-error{color:var(--text-error)}.BC-prev-next-view .BC-next-prev-item{padding:.25rem}.BC-prev-next-view .BC-next-prev-item .BC-field{padding-left:.25rem;padding-right:.25rem}.BC-search-input-container{padding:var(--size-2-2) var(--size-4-2)}.BC-search-input-container input[type=search]{width:100%}.BC-codeblock-markmap svg foreignObject div{color:var(--text-normal)}.bc-date-note-setup-warning{background:var(--background-modifier-error);color:var(--text-error);border-radius:4px;margin-bottom:12px;padding:8px 12px}@property --tw-border-style{syntax:"*";inherits:false;initial-value:solid}@property --tw-blur{syntax:"*";inherits:false}@property --tw-brightness{syntax:"*";inherits:false}@property --tw-contrast{syntax:"*";inherits:false}@property --tw-grayscale{syntax:"*";inherits:false}@property --tw-hue-rotate{syntax:"*";inherits:false}@property --tw-invert{syntax:"*";inherits:false}@property --tw-opacity{syntax:"*";inherits:false}@property --tw-saturate{syntax:"*";inherits:false}@property --tw-sepia{syntax:"*";inherits:false}@property --tw-drop-shadow{syntax:"*";inherits:false}@property --tw-drop-shadow-color{syntax:"*";inherits:false}@property --tw-drop-shadow-alpha{syntax:"<percentage>";inherits:false;initial-value:100%}@property --tw-drop-shadow-size{syntax:"*";inherits:false}

.obsidian/plugins/default-template/manifest.json

@@ -1,8 +1,8 @@
 {
 	"id": "default-template",
 	"name": "Default Template",
-	"version": "1.2.4",
-	"minAppVersion": "0.15.0",
+	"version": "1.2.6",
+	"minAppVersion": "1.4.10",
 	"description": "Automatically apply templates to new notes with user-configurable template selection.",
 	"author": "raeperd",
 	"authorUrl": "https://github.com/raeperd",

.obsidian/plugins/notebook-navigator/data.json

@@ -534,7 +534,8 @@
     "micrometa",
     "obsidan_export",
     "pocket",
-    "-#s"
+    "-#s",
+    "o"
   ],
   "rootPropertyOrder": []
 }

.obsidian/plugins/obsidian-day-planner/manifest.json

@@ -1,7 +1,7 @@
 {
   "id": "obsidian-day-planner",
   "name": "Day Planner",
-  "version": "0.28.0",
+  "version": "0.30.0",
   "minAppVersion": "0.16.0",
   "description": "A day planner with clean UI and readable syntax",
   "author": "James Lynch, continued by Ivan Lednev",

.obsidian/plugins/obsidian-latex-suite/data.json

@@ -3,7 +3,7 @@
   "snippetVariables": "{\n\t\"${GREEK}\": \"alpha|beta|gamma|Gamma|delta|Delta|epsilon|varepsilon|zeta|eta|theta|vartheta|Theta|iota|kappa|lambda|Lambda|mu|nu|xi|omicron|pi|rho|varrho|sigma|Sigma|tau|upsilon|Upsilon|phi|varphi|Phi|chi|psi|omega|Omega\",\n\t\"${SYMBOL}\": \"parallel|perp|partial|nabla|hbar|ell|infty|oplus|ominus|otimes|oslash|square|star|dagger|vee|wedge|subseteq|subset|supseteq|supset|emptyset|exists|nexists|forall|implies|impliedby|iff|setminus|neg|lor|land|bigcup|bigcap|cdot|times|simeq|approx\",\n\t\"${MORE_SYMBOLS}\": \"leq|geq|neq|gg|ll|equiv|sim|propto|rightarrow|leftarrow|Rightarrow|Leftarrow|leftrightarrow|to|mapsto|cap|cup|in|sum|prod|exp|ln|log|det|dots|vdots|ddots|pm|mp|int|iint|iiint|oint\"\n}\n",
   "snippetsEnabled": true,
   "snippetsTrigger": "Tab",
-  "snippetNextTabstopTrigger": "Shift-RightArrow",
+  "snippetNextTabstopTrigger": "Tab",
   "snippetPreviousTabstopTrigger": "Shift-Tab",
   "suppressSnippetTriggerOnIME": true,
   "suppressIMEWarning": false,

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

@@ -8,7 +8,7 @@
   "lineWidth": 40,
   "lineWidthWide": 50,
   "maxWidth": 98,
-  "textNormal": 22,
+  "textNormal": 28,
   "textSmall": 18,
   "imgGrid": false,
   "imgWidth": "img-default-width",

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

@@ -5,7 +5,7 @@
     {
       "id": 1,
       "name": "Ma bibliothèque",
-      "lastUpdate": 1777592858082
+      "lastUpdate": 1780077499649
     }
   ],
   "renderCitations": true,

.obsidian/plugins/obsidian42-brat/manifest.json

@@ -1,11 +1,11 @@
 {
 	"id": "obsidian42-brat",
 	"name": "BRAT",
-	"version": "2.0.4",
+	"version": "2.0.8",
 	"minAppVersion": "1.11.4",
-	"description": "Easily install a beta version of a plugin for testing.",
+	"description": "Easily install plugin beta versions for testing.",
 	"author": "TfTHacker",
-	"authorUrl": "https://github.com/TfTHacker/obsidian42-brat",
+	"authorUrl": "https://github.com/TfTHacker",
 	"helpUrl": "https://tfthacker.com/BRAT",
 	"isDesktopOnly": false,
 	"fundingUrl": {

.obsidian/plugins/obsidian42-brat/styles.css

@@ -111,12 +111,12 @@
 
 /* Hide filtered plugin items */
 .brat-plugin-item[hidden] {
-  display: none !important;
+  display: none;
 }
 
 /* Hide filtered theme items */
 .brat-theme-item[hidden] {
-  display: none !important;
+  display: none;
 }
 
 /* Filter and button layout */
@@ -150,3 +150,33 @@
 .brat-filter-and-button .setting-item-control {
   justify-content: flex-end;
 }
+
+.brat-full-width-input {
+  width: 100%;
+}
+
+.brat-modal-divider {
+  border-top: 1px solid var(--background-modifier-border);
+  margin-top: 30px;
+}
+
+.brat-credits {
+  font-style: italic;
+}
+
+.brat-promotional-links {
+  float: right;
+}
+
+.brat-promotional-links-modal {
+  padding: 10px 15px;
+}
+
+.brat-promotional-links-settings {
+  padding: 15px;
+  margin-left: 15px;
+}
+
+.brat-promotional-links-coffee {
+  padding-left: 10px;
+}

.obsidian/types.json

@@ -100,6 +100,8 @@
     "date-birth": "date",
     "date-death": "date",
     "excerpt_of": "multitext",
-    "part": "multitext"
+    "part": "multitext",
+    "BC-tag-note-sibling-field": "text",
+    "BC-traverse-note-field": "text"
   }
 }

Excalidraw/mémoire à tore de ferrite 2024-02-15 01.02.52.excalidraw.md

@@ -7,7 +7,9 @@ tags: [excalidraw]
 ==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
 
 
-# Text Elements
+# Excalidraw Data
+
+## Text Elements
 Reset ^RoHLK7dp
 
 Set ^NORclDsY
@@ -15,662 +17,54 @@ Set ^NORclDsY
 Sense ^1Hgsf293
 
 %%
-# Drawing
-```json
-{
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+## Drawing
+```compressed-json
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 ```
 %%

S2 LOGOS.md

@@ -7,6 +7,8 @@ up:
   - "[[master LOGOS]]"
 ---
 
+
+
 ```breadcrumbs
 title: "Sous-notes"
 type: tree

Untitled 1.md

@@ -0,0 +1,5 @@
+---
+up:
+tags:
+aliases:
+---

Untitled.md

@@ -4,6 +4,4 @@ tags:
 aliases:
 ---
 
- - 
- - ? cacher le dossier attachments 
 

base de filtre.md

@@ -0,0 +1,20 @@
+---
+up:
+  - "[[filtre engendré]]"
+tags:
+  - s/maths/logique
+aliases:
+---
+
+> [!definition] [[base de filtre]]
+> Soit $X$ un ensemble infini.
+> Soit $\mathcal{B}\subseteq \mathcal{P}(X)$ une partie de $\mathcal{P}(X)$
+> $\mathcal{B}$ est une **base de filtre** sur $X$ si :
+>  - $\emptyset \notin \mathcal{B}$
+>  - $\mathcal{B}$ est stable par intersection : $\forall A, B \in \mathcal{B},\quad A \cap B \in \mathcal{B}$
+^definition
+
+# Propriétés
+
+# Exemples
+

calcul propositionnel.md

@@ -0,0 +1,16 @@
+---
+up:
+  - "[[logique]]"
+tags:
+  - s/maths/logique
+aliases:
+---
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```

classifier et diviser les personnes.md

@@ -1,12 +1,12 @@
 ---
-id: classifier et diviser les personnes
-aliases: []
-tags: []
-alias:
-  - classifier les personnes
+up: "[[étapes d'un génocide]]"
+tags:
+  - "#s/science/histoire"
+  - "#s/philosophie"
+  - "#s/science/zetetique"
+aliases:
+  - "classifier les personnes"
 ---
-up:: [[étapes d'un génocide]]
-#s/science/histoire #s/philosophie #s/science/zetetique 
 
 Classifier les gens, par *race*, par croyances, physique...
 

consistance sémantique.md

@@ -2,6 +2,6 @@
 
 ---
 
-Dans l'[[logique approche sémantique]], une [[théorie logique]] est _consistante_ (ou encore [[satisfaisable]]) ssi elle possède au moins un [[modèle]]. Dans le cas contraire, la théorie est dire inconsistante.
+Dans l'[[logique approche sémantique]], une [[théorie logique]] est _consistante_ (ou encore [[satisfaisable]]) ssi elle possède au moins un [[théorie des modèles . modèle]]. Dans le cas contraire, la théorie est dire inconsistante.
 Une théorie inconsistante est considérée comme de peu d'intérêt
 

conséquence formelle.md

@@ -0,0 +1,5 @@
+---
+up:
+tags:
+aliases:
+---

conséquence sémantique.md

@@ -2,7 +2,7 @@
 
 ---
 
-Une [[proposition]] $B$ est la _conséquence sémantique_ d'une [[proposition]] $A$ ssi **tout [[modèle]] de $A$ est un [[modèle]] de $B$**.
+Une [[proposition]] $B$ est la _conséquence sémantique_ d'une [[proposition]] $A$ ssi **tout [[théorie des modèles . modèle]] de $A$ est un [[théorie des modèles . modèle]] de $B$**.
 
 # Définition
 $A\models B \iff \forall x, x\models A \implies x\models B$

contradiction.md

@@ -1,7 +1,7 @@
 #s/maths/logique
 
 ---
-Une contradiction est une [[proposition]] qui n'admet **aucun [[modèle]]**.
+Une contradiction est une [[proposition]] qui n'admet **aucun [[théorie des modèles . modèle]]**.
 C'est-à-dire qu'elle n'est vraie pour aucune [[interprétation]].
 On dit aussi que cette proposition est _insatifaisable_
 

daily/2026-02-17.md

@@ -1,8 +1,8 @@
 # Todo
 
 - [ ] #task trouver pompe à vélo
-- [ ] #task acheter billet de train 🔺
-- [ ] #task mail prof de computational semantics
+- [x] #task acheter billet de train 🔺 ✅ 2026-05-31
+- [x] #task mail prof de computational semantics ✅ 2026-05-31
     - [ ] possible de suivre le cours maintenant ?
     - [ ] question sur le lab 1 (is my solution too hacky ?)
 

daily/2026-05-31.md

@@ -0,0 +1,20 @@
+# Todo
+
+```tasks
+due 2026-05-31
+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 2026-05-31
+short mode
+```
+# I am gratefull to
+

démonstration.md

@@ -3,4 +3,4 @@
 ---
 Une _démonstration formelle_ est l'application successive de plusieurs [[règle d'inférence|règles d'inférence]] à partir d'un ensemble [[axiome|d'axiomes]] ou de [[théorème|théorèmes]] déjà démontrés.
 
-Une Démonstration produit systématiquement de nouveaux théorèmes qui sont la [[conséquence formelle]]
+Une Démonstration produit systématiquement de nouveaux théorèmes qui sont la [[conséquence]]

désintégration audioactive.md

@@ -24,8 +24,9 @@ header-auto-numbering:
 
 <div class="page-break" style="page-break-before: always;"></div>
 
+# Introduction
 
-La *désintégration audioactive* (aussi appellée *suite* look-and-say, ou *suite de Conway*) est une suite d'entiers strictement positifs. Elle à notamment été étudiée par John H. Conway, bien qu'elle n'aie pas été décrite d'abord par lui (elle lui à été présentée par un étudiant, comme il l'indique dans une interview publiée en 2024 : [Look-and-Say Numbers (feat John Conway) - Numberphile](https://www.youtube.com/watch?v=ea7lJkEhytA)).
+La *désintégration audioactive* (aussi appellée *suite* look-and-say, ou *suite de Conway*) est une suite d'entiers strictement positifs. Elle a notamment été étudiée par John H. Conway, bien qu'elle n'aie pas été décrite d'abord par lui (elle lui a été présentée par un étudiant, comme il l'indique dans une interview publiée en 2024 : [Look-and-Say Numbers (feat John Conway) - Numberphile](https://www.youtube.com/watch?v=ea7lJkEhytA)).
 
 Son principe est assez simple : étant donné un nombre, on produit le suivant en "lisant" le précédent. Par exemple "11" se lit "deux uns" ce qui donne "21" ; à son tour "21" se lit "un deux, un un" soit "1211" et ainsi de suite :
  - $1 \longrightarrow \text{un } 1$
@@ -39,27 +40,57 @@ Son principe est assez simple : étant donné un nombre, on produit le suivant e
 
 La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^{\gamma}d^{\delta}\cdots \longrightarrow \alpha a\beta b\gamma c\delta d\cdots$
 
+Pour donner une défintion précise et reproductible de la suite (et pour vérifier certains calculs) on pourra utiliser la définition suivante :
+
+```python
+def chaine_suivante(ch: list[int]) -> list[int]:
+    resultat = []  # future chaine
+    decompte = 0  # nombre de répétitions
+    index = 0  # index du parcours
+    valeur = ch[index]  # valeur à compter
+    while index + 0 < len(ch):
+        if valeur == ch[index]:
+            decompte += 1  # incrémenter si la valeur est la même
+        else:
+            # enregister decompte,valeur dans résusltat si la valeur est nouvelle
+            resultat.append(decompte)
+            resultat.append(valeur)
+            valeur = ch[index]
+            decompte=1
+        index += 1
+    resultat.append(decompte)
+    resultat.append(valeur)
+    return resultat
+```
+
+
+<div class="page-break" style="page-break-before: always;"></div>
+
 # Notations
- - Comme les éléments de la suite sont plutôt des suites finies de chiffres que des nombres uniques, on appellera "chaine" un terme de la suite.
- - On assimilera toujours les éléments d'une chaine à des chiffres strictement positifs.
- - On se permettra de confondre "chaine" et "sous-chaine" (sous-ensemble de chiffres consécutifs d'une chaine) lorsque l'on traitera de propriétés locales.
- - 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
+
+ - Comme les éléments de la suite sont plutôt des suites finies de chiffres que des nombres uniques, on appellera **chaine** un terme de la suite.
+ - On assimilera toujours les éléments d'une chaine à des chiffres strictement positifs. Le théorème du jour 2 explicitera pourquoi $0$ et les nombres supérieurs à 10 n'ont pas d'intérêt particulier.
+ - On se permettra de confondre **chaine** et **sous-chaine** (sous-ensemble de chiffres consécutifs d'une chaine) lorsque l'on traitera de propriétés locales.
+ - On appellera **dérivation** le fait d'appliquer la règle de passage d'une chaine à la suivante.
+ - $L \longrightarrow L'$ signifie que $L$ dérive en $L'$ par désintégration audioactive
      - On note aussi $L \longrightarrow L' \longrightarrow L'' \longrightarrow \cdots$ pour $L \longrightarrow L'$ et $L' \longrightarrow L''$ et $L'' \longrightarrow \cdots$
+     - On peut ajouter une condition : $L \xrightarrow{n\neq 2} L'$ signifie que $L$ dérive en $L'$ si $n \neq 2$.
  - $L_{n}$ est le $n^{\text{ème}}$ *descendant* de $L$ (le résultat de $n$ dérivations de $L$)
-     - évidemment : $L_0 = L$ et $L_{n} \to L_{n+1}$
+     - évidemment : $L_0 = L$ et $L_{n} \longrightarrow L_{n+1}$
      - i on peut noter $L \xrightarrow{n} L_{n}$
- - On utilise $[$ et $]$ pour dénoter la "véritable fin" des sous-chaines
+ - 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 $122111 \longrightarrow \dots 12231 \dots$
+ - On utilise $[$ et $]$ pour dénoter le *véritable début* et la *véritable fin* des sous-chaines
      - = $[11222$ correspond à $11 222\cdots$ autrement dit, la chaine continue potentiellement à droite, mais pas à gauche
  - On utilise les puissances pour la répétition
      - = $3^{4}2^{1}1^{5} = 333211111$
      - i on prends toujours la plus grande puissance possible (par exemple, $11111$ ne sera jamais noté comme $1^{2}1^{3}$) (cela est important pour les premiers théorèmes)
  - $X$ désigne un chiffre arbitraire (non nul)
+     - i si on écrit $[a^{\alpha}X^{\beta}$, on suppose que $a \neq X$ et que la suite de la chaine (s'il y en a une) n'est pas directement un $X$.
      - = $X^{0}a^{\alpha}b^{\beta}c^{\gamma}$ correspond à $[a^{\alpha}b^{\beta}c^{\gamma}$
      - = $a^{\alpha}b^{\beta}c^{\gamma}X^{0}$ correspond à $a^{\alpha}b^{\beta}c^{\gamma}]$
-     - = $2^{2}X^{2}$ correspond à l'une de : $2^{2}1^{2},\quad 2^{2}3^{2},\quad 2^{2}4^{2},\quad 2^{2}5^{2}, \dots$ (mais pas à $2^{2}2^{2} = 2^{4}$)
-     - = $2^{X}$ correspond à l'une de : $2,\quad 2^{2},\quad 2^{3},\quad 2^{4}, \dots$ (mais ne peut pas être vide)
+     - = $2^{2}X^{2}$ correspond à l'une des chaines : $2^{2}1^{2},\quad 2^{2}3^{2},\quad 2^{2}4^{2},\quad 2^{2}5^{2}, \dots$ (mais pas à $2^{2}2^{2} = 2^{4}$)
+     - = $2^{X}$ correspond à l'une des chaines : $2,\quad 2^{2},\quad 2^{3},\quad 2^{4}, \dots$ (mais ne peut pas être vide)
  - $\neq n$ 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 $2$
@@ -76,13 +107,16 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
  
 # Propriétés
 
-> [!proposition]+ conséquence du regroupement
+> [!proposition] conséquence du regroupement
 > Pour une étape :
 > $a^{\alpha}b^{\beta}c^{\gamma}d^{\delta}\cdots \longrightarrow \alpha a\beta b\gamma c\delta d\cdots$
 > Il est évident que :
 > $a\neq b,\quad b\neq c,\quad c\neq d,\dots$
 >  - dem Cela découle directement du fait que l'on choisit, à chaque fois, les plus grands $\alpha, \beta, \gamma, \delta\dots$ possibles
 ^regroupement
+
+La localité de la fonction de dérivation (le fait que les chiffres éloignés ne s'influencent pas mutuellement dans la dérivation) sera très utile lorsque l'on considèrera les sous-chaines.
+
 ## Atomes
 
 > [!definition] Découpage
@@ -104,7 +138,7 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
 
 ## Théorèmes préliminaires
 
-> [!proposition]+ Théorème du jour 1
+> [!proposition] Théorème du jour 1
 > Les morceaux de type :
 >  1. $,ax,bx,$
 >  2. $x^{\geq 4}$
@@ -121,15 +155,15 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
 > >       $,\underbrace{xx,xx,\dots,x x}_{\frac{n}{2} \text{ répétitions}},$ et au minimum $,xx,xx,$ pour $n = 4$. Il est évident que, dans ce cas, la dérivation ne peut pas donner cela puisque l'on aurait du regrouper tous ces $x$ : $x^{2\times x}$ n'est pas dérivé en $xx,xx$ mais en $(2\times x)x$
 > >       L'autre parsing possible est $x,\underbrace{xx, \dots, xx}_{\frac{n}{2}-1 \text{ répétitions}},x$ ce qui donne, à nouveau, le même résultat : $,x,x^{k},x,$ n'aurait pas du être dérivé ainsi, mais en $(k+2)x$
 > >     - si $n$ est impair : ($n\geq 5$)
-> >       A nouveau, ni $,\underbrace{xx,xx,\dots,xx}_{\left\lfloor \frac{n}{2} \right\rfloor \text{ répétitions}},x,$ ni $[x,\underbrace{xx,xx, \dots, x x}_{\lfloor \frac{n}{2} \rfloor \text{ répétitions}},$ ne sont des dérivations correctes
-> > 2. $x^{3}y^{3}$
+> >       À nouveau, ni $,\underbrace{xx,xx,\dots,xx}_{\left\lfloor \frac{n}{2} \right\rfloor \text{ répétitions}},x,$ ni $[x,\underbrace{xx,xx, \dots, x x}_{\lfloor \frac{n}{2} \rfloor \text{ répétitions}},$ ne sont des dérivations correctes
+> > 1. $x^{3}y^{3}$
 > >    Encore une fois, considérons les parsing possibles :
 > >     - $,xx,xy,yy,$ ne peut pas exister, puisque $,xy,yy,$ aurait du être dérivé en un $,ky,$
 > >     - $[x,xx,yy,y]$ ne peut pas exister puisque $\alpha x,x x$ aurait du être dérivé en $(\alpha+x) x$
 > > Cela montre bien qu'aucune de ces formes ne peut exister après dérivation.
 ^thm-jour-1
 
-> [!proposition]+ Théorème du jour 2
+> [!proposition] Théorème du jour 2
 >  - Aucun chiffre $\geq 4$ ne peut apparaître au jour 2 ou ensuite (sauf conservation d'un chiffre qui était déjà présent).
 >  - Un morceau $3 X 3$ (en particulier $3^{3}$) ne peut pas apparaître dans aucune chaîne âgée d'au moins 2 jours.
 > 
@@ -140,7 +174,7 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
 > >    On doit donc nécessairement parser $3X 3$ comme $,3x,3y,$. Pour obtenir $,3x,3y,$, on doit avoir obtenu $x^{3}y^{3}$ au jour précédent, ce qui est impossible dès le jour 1 (par le [[désintégration audioactive#^thm-jour-1|Théorème du jour 1]]). Cela montre bien que $3X 3$ est impossible dès le jour 2. 
 ^thm-jour-2
 
-> [!proposition]+ Théorème du début 
+> [!proposition] Théorème du début 
 > Soit $R$ un morceau d'une chaîne âgée de 2 jours ou plus.
 > Le début de ses descendants finira toujours par se constituer en l'un des cycles suivants :
 >  - $\overparen{[ \; ]} \longrightarrow [\;] \longrightarrow [\;] \longrightarrow \cdots$
@@ -148,7 +182,7 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
 >  - $\overparen{[1^{1}X^{1} \longrightarrow [1^{3} \longrightarrow [3^{1}X^{\neq 3}} \longrightarrow [1^{1}X^{1} \longrightarrow \cdots$
 >  - $\overparen{[2^{2}1^{1}X^{1} \longrightarrow [2^{2}1^{3} \longrightarrow [2^{2}3^{1}X^{\neq 3}} \longrightarrow [2^{2}1^{1}X^{1} \longrightarrow \cdots$
 > 
-> > [!démonstration]+ Démonstration
+> > [!démonstration]- Démonstration
 > > Explorons les valeurs possibles de $R$ en supposant que $R$ est âgée de 2 jours ou plus, et ne commence pas par $2^{2}$.
 > > Eliminons à chaque fois les valeurs impossibles (notamment en utilisant les théorèmes [[désintégration audioactive#^thm-jour-1|du jour 1]] et [[désintégration audioactive#^thm-jour-2|du jour 2]]) :
 > >  - Si $R$ commence par $1$
@@ -268,7 +302,7 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
 > > ![[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 de découpage
+> [!proposition] théorème de découpage
 > Une chaîne $LR$ âgée de 2 jours ou plus se découpe en $L \cdot R$ seulement dans ces cas :
 > 
 > | L         | R                                                                                             |
@@ -283,7 +317,7 @@ La règle définissant la suite peut alors être notée : $a^{\alpha}b^{\beta}c^
  ^theoreme-decoupage
 ^theoreme-de-decoupage
 
-> [!proposition]+ Théorème de la fin
+> [!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]]
 > 
@@ -348,7 +382,7 @@ On a défini plus tôt ce qu'était un [[désintégration audioactive#^def-atome
 On peut alors décrire 92 atomes. Il est trivial de montrer que chacune de ces 92 chaînes est bien un atome (à l'aide du [[désintégration audioactive#^theoreme-de-decoupage|théorème de découpage]]).
 Conway leur donne des noms d'éléments (de l'hydrogène à l'uranium, ce qui fait bien 92 éléments).
 
-> [!info]- Liste des éléments
+> [!info] Liste des éléments
 > | $n$ | nom | éléments dans la dérivée          | chaîne                                     | dérivée                                              |
 > | ------- | --- | ---------------- | ------------------------------------------ | ---------------------------------------------------- |
 > | 1       | H   | H (stable)       | 22                                         | 22                                                   |
@@ -450,12 +484,12 @@ Conway leur donne des noms d'éléments (de l'hydrogène à l'uranium, ce qui fa
 ## Théorèmes sur les éléments
 
 
-> [!proposition]+ Théorème chimique
+> [!proposition] Théorème chimique
 >  1. les descendents de chacun des 92 éléments sont des composés de ces éléments
 >     Autrement dit : $\forall A \text{ élément},\quad A \longrightarrow X_1\cdot X_2\cdot \cdots \quad \text{ où }X_1,X_2,\dots \text{ sont des éléments}$
->  2. Tous les descendants suffisament âgés de chacun des éléments (autres que l'Hydrogène $22$)  contiennent simultanément les 92 éléments.
+>  2. Tous les descendants suffisament âgés de chacun des éléments (autres que l'Hydrogène $22$)  contiennent simultanément les 92 éléments (et on peut borner le nombre de dérivations nécessaires pour atteindre cet état).
 >     Autrement dit : $\forall A \text{ élément},\quad \exists n\in \mathbb{N},\quad A \longrightarrow^{(n)} X \quad \text{où } X \text{ contient tous les 92 éléments}$
->  3. Les descendants de toutes les chaînes autres que $[\;]$ et $[22]$ finissent par contenir les 92 éléments simultanément.
+>  3. Les descendants de toutes les chaînes autres que $[\;]$ et $[22]$ finissent (après un nombre borné de dérivations) par contenir les 92 éléments simultanément.
 >
 > > [!démonstration]- Démonstration
 > >  1. Cela est montré par la table des éléments donnée plus haut. Le lecteur sceptique pourra vérifier la correction des dérivations.
@@ -487,19 +521,218 @@ Conway leur donne des noms d'éléments (de l'hydrogène à l'uranium, ce qui fa
 > >  1. Soit $L$ une chaîne différente de $[\;]$ ou $[22]$.
 > >     Si $L$ est de la forme $L'2^{2}]$, on considère $L'$ à la place de $L$ (on ignore le $2^{2}]$). On sait que l'on peut faire ce découpage : $(X\neq 2)\cdot 2^{2}] \longrightarrow (X \neq 2)\cdot 2^{2}$.
 > >     Ainsi, on peut affirmer que $L$ correspond soit au cycle $(1)$, soit au cycle $(2)$ dans le théorème de la fin. En observant la preuve du théorème de la fin, on remarque l'apparition du Calcium (la chaîne $\color{crimson}12$ notée $\ce{Ca}$ et indiquée en <span style="color: crimson">rouge</span>) dans les deux cycles, ce qui montre qu'un descendant assez avancé de $L$ contient du Calcium.
+> >     Il est manifeste que l'apparition du Calcium se fait en un nombre borné d'étapes.
 > >     La propriété 2. permet de conclure.
 
-
 > [!definition] Chaine commune
 > Une **chaine commune** est une chaine exclusivement composée d'éléments.
 
+> [!proposition] Théorème arithmétique
+> 4. Les longueurs de toutes les chaines communes (autres que les cas triviaux $[\;]$ et $[22]$) augmentent selon une progression géométrique, avec une même raison $\lambda > 1$.
+> 5. Les abondances relatives des éléments dans ces chaines convergent vers une valeur fixe, strictement positive pour tous les éléments.
+>
+> > [!démonstration]- Démonstration
+> > On note $\operatorname{lg}[L]$ la *longueur* d'une chaine (son nombre de chiffres) et $\operatorname{ne}[L]$  le *nombre d'éléments* (en comptant les doublons) contenus dans une chaine $L$.
+> > Par exemple, $\operatorname{lg}[3223] = 4$ et $\operatorname{ne}[3223] = \operatorname{ne}[\ce{U \cdot H  \cdot U}] = 3$.
+> > Comme tous les éléments ont une comprise entre $1$ et $42$, on peut assimiler la longueur au nombre d'éléments dans le calcul de $\lambda$. Formellement, si $L_0$ est une chaine commune :
+> > $\forall n,\quad \operatorname{ne}[L_{n}] \leq \operatorname{lg}[L_{n}]  \leq 48  \cdot \operatorname{ne}[L_{n}]$
+> > Donc :
+> > $\displaystyle\forall n,\quad \frac{\operatorname{ne}[L_{n+1}]}{\operatorname{ne}[L_{n}]} \leq \frac{\operatorname{lg}[L_{n+1}]}{\operatorname{lg}[L_{n}]} \leq \frac{48 \cdot \operatorname{ne}[L_{n+1}]}{48\cdot \operatorname{ne}[L_{n}]}$
+> > Ce qui montre bien que $\forall n,\quad \dfrac{\operatorname{lg}[L_{n+1}]}{\operatorname{lg}[L_{n}]} = \dfrac{\operatorname{ne}[L_{n+1}]}{\operatorname{ne}[L_{n}]}$.
+> > Or, comme $\lambda$ est l'éventuelle limite de $\dfrac{\operatorname{lg}[L_{n+1}]}{\operatorname{lg}[L_{n}]}$, on pourra aussi bien calculer $\lambda$ en considérant la longueur que le nombre d'éléments.
+> > 
+> >  1. Soit $L_0$ une chaine commune, notons $\#_{E_{k}}[L_0]$ le nombre d'occurences de l'élément $E_{k}$ dans $L_0$.
+> >     Par exemple $\operatorname{ne}[L_{n}] =\sum\limits_{k=1}^{92} \#_{E_{k}}[L_n]$.
+> >     Représentons alors $L_{n}$ comme un vecteur de $\mathbb{N}^{92}$ : la $k^{\text{ème}}$ coordonnée sera le nombre d'occurence de $E_{k}$ dans $L_{n}$. On notera $v^{(n)} =\operatorname{vec}[L_{n}] = (\#_{E_1}[L_{n}],\quad \#_{E_2}[L_{n}],\quad \#_{E_{3}}[L_{n}], \dots,\quad \#_{E_{92}}[L_{n}])$.
+> >     Autrement dit :
+> >     $\forall k \in [\![ 1; 92]\!],\quad v^{(n)}{}_{k} = \operatorname{vec}[L_{n}]_{k} = \#_{E_{k}}[L_{n}]$
+> >     $v^{(n)}$ est donc le vecteur comptant les occurences des éléments dans $L_{n}$.
+> >     Par la propriété 1. du théorème chimique, on sait que cette représentation vectorielle est «&nbsp;suffisante&nbsp;» puisque l'on peut passer de $v^{(n)}$ à $v^{(n+1)}$ en faisant un comptage adéquat de la nouvelle quantité de chaque élément (et cela décrit bien l'entièreté du contenu de $L_{n+1}$) :
+> >     $\forall k \in [\![1; 92]\!],\quad v^{(n+1)}{}_{k} = \sum\limits_{i=1}^{92}v^{(n)}{}_{k}\cdot\#_{E_{k}}[E_{i}{}']$
+> >     On remarque que cette formule ressemble à celle qui définit la multiplication d'une matrice par un vecteur :
+> >     $(v\cdot M)_{k} = \sum\limits_{i} v_{k} \cdot M_{i,k}$
+> >     En particulier, pour le passage de $v^{(n)}$ à $v^{(n+1)}$, la matrice sera définie par :
+> >     $\forall i,j \in [\![1, 92]\!],\quad M_{i, j} = \#_{E_j}[E_{i}{}']$ avec $M \in \mathcal{M}_{92}(\mathbb{N})$
+> >     Ainsi, on obtient $\boxed{v^{(n+1)} = v^{(n)}\cdot M = v^{(0)}\cdot M^{n+1}}$
+> >     La propriété définissant $\lambda$ peut alors se formuler comme $v^{(0)}\cdot M^{n+1} = \lambda \cdot v^{(0)}\cdot M^{n} \iff v^{(0)} \cdot M = \lambda \cdot v^{(0)}$ (en négligeant les formalismes de passage à la limite). Cela indique que $\lambda$ doit être une valeur propre de $M$.
+> >     Pour être plus formel, on suppose à l'inverse que $\Lambda$ est une valeur propre de $M$ (celle de plus grand module) correspondant au vecteur propre $v^{p}$. On remarque alors que $v^{p}M^{n}$ est proportionnel à $\Lambda^{n}$ (par définition des valeurs propres), autrement dit $v^{p}M^{n}= \Lambda^{n}\cdot v^{p}$. 
+> >     Le théorème de Perron-Froenbius nous permet d'affirmer que, puisque $M$ est carrée et positive, la valeur propre de plus grand module,$\Lambda$, est positive et unique. De là, on tire le fait que $v^{(0)}M^{n} \leq \Lambda^{n}\cdot v^{p}$.
+> >     Le théorème chimique permet d'affirmer que, asymptotiquement, la croissance de $(\operatorname{ne}[L_{n}])_{n \in \mathbb{N}}$ sera au moins égale à chacune de celles engendrée par un vecteur contenant un unique élément.
+> >     Puisque chaque élément engendre tous les autres, et puisque les 92 vecteurs représentant un élément seul forment une base de $\mathbb{N}^{92}$, et par le théorème chimique, on comprend que la croissance limite de raison $\lambda$ sera asymptotiquement atteinte par $(v^{(n)})_{n \in \mathbb{N}}$.
+> >     Il est évident que $\lambda > 1$ par définition de la suite.
+> >     Cela montre la propriété recherchée.
 
-> [!proposition]+ Théorème arithmétique
-> 1. Les longueurs de toutes les chaines communes (autres que les cas triviaux $[\;]$ et $[22]$) augmentent selon une progression géométrique, avec une même raison $\lambda > 1$.
-> 2. Les abondances relatives des éléments dans ces chaines convergent vers une valeur fixe, strictement positive pour tous les éléments.
-> > [!démonstration]+ Démonstration
-> > On note $\operatorname{lg}[L]$ la *longueur* d'une chaine (son nombre de chiffres) et $\operatorname{ne}[L]$  le *nombre d'éléments* contenus dans une chaine $L$.
-> > Comme tous les éléments ont une comprise entre $1$ et $42$
+> [!proposition] Valeur de $\lambda$ et croissance de la suite
+> L'annexe 1 fournit le code permettant de calculer une approximation de $\lambda$.
+> L'approximation obtenue est $\lambda \approx  1.3035772690343037$
+> Il est évident que $\lambda$ est un nombre algébrique de degré $92$. Il se trouve qu'il est même de degré 71 [voir @OpenProblemsCommunication1987 p.188].
+> --- 
+> Puisque la longueur $lg[L_{n}]$ et la valeur de $L_{n}$ en tant que nombre sont reliés par un encadrement logarithmique : $\operatorname{lg}[L_{n}] \leq \log_{10}(L_{n}) < \operatorname{lg}[L_{n}] + 1$, on peut en déduire assez directement que $L_{n} = O(10^{(\lambda^{n})})$
+
+> [!proposition] Théorème cosmologique
+> Toute chaine (autre que $[\;]$ et $[22]$) finit, après un nombre borné de dérivations, par engendrer des chaines communes. Cela permet d'appliquer le théorème chimique à toutes les chaines.
+> > [!démonstration]- Démonstration
+> > La démonstration serait trop complexe pour le cadre de ce devoir. Conway lui-même ne l'a pas publiée dans son article *The weird and wonderful chemistry of audioactive decay*.
 > > 
-> >  1. 
+> > La preuve originale de Conway et ses collègues contenait un grand nombre de cas à prouver. La preuve originale et une seconde preuve ont été perdues par Conway et ses collèges[^cos-thm-lost].
+> > Des preuves ont été produites par la suite, par exemple celle-ci se basant sur l'étude d'automates en lien avec la suite : [@lairezConwaysCosmologicalTheorem2025].
+> > Une approche peut-être plus similaire à celle de Conway et ses collègues serait peut être de tester algorithmiquement les cas pertinents[^preuve-algo].
 > > 
+
+
+[^cos-thm-lost]:  «&nbsp;Proof of the Cosmological Theorem would fill the rest of this book! Richard Parker and I found a proof over a period of about a month of very intensive work (or, rather, play!). We first produced a very subtle and complicated argument, which (almost) reduced the problem to tracking a few hundred cases, and then handled these on dozens of sheets of paper (now lost). Mike Guy found a simpler proof that used tracking and backtracking in roughly equal proportions. Guy’s proof still filled lots of pages (almost all lost) but had the advantage that it found the longest-lived of the exotic elements, namely, the isotopes of Merhuselum (2233322211n ; see Figure 2). Can you find a proof in only a few pages? Please!&nbsp;» [@OpenProblemsCommunication1987 p.]
+
+[^preuve-algo]: C'est ce que font Ekhad & Zeilberger : «&nbsp;[We compute] iteratively all non-splittable string of length $i$ ($i = 1, 2, \dots$) that might concievably be substrings ('chunks') of an atom in the splitting of a 9-day-old-string (by backtracking, examining its possible ancestors up to (at most) 8 days back and rejecting those that lead to grammatically incorrect ancestors [...]). Every time a string of length $i$ is accepted, its longevity (number of days it takes to decay to stable or transuranic elements) is computed, and checked whether it is finite. The maximal longevity turned out to be 20. The program halts if and when $i$ is reached for which the set of such concievable string of length $i$ is empty.&nbsp;» [@ZeilbergerDoronCosmologicalTheorem]
+
+
+<div class="page-break" style="page-break-before: always;"></div>
+
+# Annexes
+
+## Annexe 0 - Au sujet du présent document
+
+Ce document est inspiré de l'article « *The weird and wonderful chemistry of audioactive decay* » [@coverOpenProblemsCommunication1987] de John H. Conway, dont il tire son ordre démonstratif ainsi que certaines notations. Cependant, je ne l'ai pas produit en «&nbsp;fait confiance&nbsp;» à l'article original : j'ai reproduit chacun des calculs explicités, modifié certaines preuves et explicité des points que Conway avait laissé au lecteur.
+
+
+## Annexe 1 - Code source utilisé pour le calcul
+
+```python
+import numpy as np
+
+
+# Liste de dictionnaires représentant les éléments
+ELEMENTS = [{"num": 1,  "name": "H",  "deriv": ["H"]}, #{{{
+            {"num": 2,  "name": "He", "deriv": ["Hf","Pa","H","Ca","Li"]},
+            {"num": 3,  "name": "Li", "deriv": ["He"]},
+            {"num": 4,  "name": "Be", "deriv": ["Ge","Ca","Li"]},
+            {"num": 5,  "name": "B",  "deriv": ["Be"]},
+            {"num": 6,  "name": "C",  "deriv": ["B"]},
+            {"num": 7,  "name": "N",  "deriv": ["C"]},
+            {"num": 8,  "name": "O",  "deriv": ["N"]},
+            {"num": 9,  "name": "F",  "deriv": ["O"]},
+            {"num": 10, "name": "Ne", "deriv": ["F"]},
+            {"num": 11, "name": "Na", "deriv": ["Ne"]},
+            {"num": 12, "name": "Mg", "deriv": ["Pm", "Na"]},
+            {"num": 13, "name": "Al", "deriv": ["Mg"]},
+            {"num": 14, "name": "Si", "deriv": ["Al"]},
+            {"num": 15, "name": "P",  "deriv": ["Ho", "Si"]},
+            {"num": 16, "name": "S",  "deriv": ["P"]},
+            {"num": 17, "name": "Cl", "deriv": ["S"]},
+            {"num": 18, "name": "Ar", "deriv": ["Cl"]},
+            {"num": 19, "name": "K",  "deriv": ["Ar"]},
+            {"num": 20, "name": "Ca", "deriv": ["K"]},
+            {"num": 21, "name": "Sc", "deriv": ["Ho", "Pa", "H", "Ca", "Co"]},
+            {"num": 22, "name": "Ti", "deriv": ["Sc"]},
+            {"num": 23, "name": "V",  "deriv": ["Ti"]},
+            {"num": 24, "name": "Cr", "deriv": ["V"]},
+            {"num": 25, "name": "Mn", "deriv": ["Cr", "Si"]},
+            {"num": 26, "name": "Fe", "deriv": ["Mn"]},
+            {"num": 27, "name": "Co", "deriv": ["Fe"]},
+            {"num": 28, "name": "Ni", "deriv": ["Zn", "Co"]},
+            {"num": 29, "name": "Cu", "deriv": ["Ni"]},
+            {"num": 30, "name": "Zn", "deriv": ["Cu"]},
+            {"num": 31, "name": "Ga", "deriv": ["Eu", "Ca","Ac","H","Ca","Zn"]},
+            {"num": 32, "name": "Ge", "deriv": ["Ho", "Ga"]},
+            {"num": 33, "name": "As", "deriv": ["Ge", "Na"]},
+            {"num": 34, "name": "Se", "deriv": ["As"]},
+            {"num": 35, "name": "Br", "deriv": ["Se"]},
+            {"num": 36, "name": "Kr", "deriv": ["Br"]},
+            {"num": 37, "name": "Rb", "deriv": ["Kr"]},
+            {"num": 38, "name": "Sr", "deriv": ["Rb"]},
+            {"num": 39, "name": "Y",  "deriv": ["Sr", "U"]},
+            {"num": 40, "name": "Zr", "deriv": ["Y","H","Ca","Tc"]},
+            {"num": 41, "name": "Nb", "deriv": ["Er", "Zr"]},
+            {"num": 42, "name": "Mo", "deriv": ["Nb"]},
+            {"num": 43, "name": "Tc", "deriv": ["Mo"]},
+            {"num": 44, "name": "Ru", "deriv": ["Eu", "Ca","Tc"]},
+            {"num": 45, "name": "Rh", "deriv": ["Ho", "Ru"]},
+            {"num": 46, "name": "Pd", "deriv": ["Rh"]},
+            {"num": 47, "name": "Ag", "deriv": ["Pd"]},
+            {"num": 48, "name": "Cd", "deriv": ["Ag"]},
+            {"num": 49, "name": "In", "deriv": ["Cd"]},
+            {"num": 50, "name": "Sn", "deriv": ["In"]},
+            {"num": 51, "name": "Sb", "deriv": ["Pm", "Sn"]},
+            {"num": 52, "name": "Te", "deriv": ["Eu", "Ca","Sb"]},
+            {"num": 53, "name": "I",  "deriv": ["Ho", "Te"]},
+            {"num": 54, "name": "Xe", "deriv": ["I"]},
+            {"num": 55, "name": "Cs", "deriv": ["Xe"]},
+            {"num": 56, "name": "Ba", "deriv": ["Cs"]},
+            {"num": 57, "name": "La", "deriv": ["Ba"]},
+            {"num": 58, "name": "Ce", "deriv": ["La", "H","Ca","Co"]},
+            {"num": 59, "name": "Pr", "deriv": ["Ce"]},
+            {"num": 60, "name": "Nd", "deriv": ["Pr"]},
+            {"num": 61, "name": "Pm", "deriv": ["Nd"]},
+            {"num": 62, "name": "Sm", "deriv": ["Pm", "Ca","Zn"]},
+            {"num": 63, "name": "Eu", "deriv": ["Sm"]},
+            {"num": 64, "name": "Gd", "deriv": ["Eu", "Ca","Co"]},
+            {"num": 65, "name": "Tb", "deriv": ["Ho", "Gd"]},
+            {"num": 66, "name": "Dy", "deriv": ["Tb"]},
+            {"num": 67, "name": "Ho", "deriv": ["Dy"]},
+            {"num": 68, "name": "Er", "deriv": ["Ho", "Pm"]},
+            {"num": 69, "name": "Tm", "deriv": ["Er", "Ca","Co"]},
+            {"num": 70, "name": "Yb", "deriv": ["Tm"]},
+            {"num": 71, "name": "Lu", "deriv": ["Yb"]},
+            {"num": 72, "name": "Hf", "deriv": ["Lu"]},
+            {"num": 73, "name": "Ta", "deriv": ["Hf", "Pa","H","Ca","W"]},
+            {"num": 74, "name": "W",  "deriv": ["Ta"]},
+            {"num": 75, "name": "Re", "deriv": ["Ge", "Ca","W"]},
+            {"num": 76, "name": "Os", "deriv": ["Re"]},
+            {"num": 77, "name": "Ir", "deriv": ["Os"]},
+            {"num": 78, "name": "Pt", "deriv": ["Ir"]},
+            {"num": 79, "name": "Au", "deriv": ["Pt"]},
+            {"num": 80, "name": "Hg", "deriv": ["Au"]},
+            {"num": 81, "name": "Tl", "deriv": ["Hg"]},
+            {"num": 82, "name": "Pb", "deriv": ["Tl"]},
+            {"num": 83, "name": "Bi", "deriv": ["Pm", "Pb"]},
+            {"num": 84, "name": "Po", "deriv": ["Bi"]},
+            {"num": 85, "name": "At", "deriv": ["Po"]},
+            {"num": 86, "name": "Rn", "deriv": ["Ho", "At"]},
+            {"num": 87, "name": "Fr", "deriv": ["Rn"]},
+            {"num": 88, "name": "Ra", "deriv": ["Fr"]},
+            {"num": 89, "name": "Ac", "deriv": ["Ra"]},
+            {"num": 90, "name": "Th", "deriv": ["Ac"]},
+            {"num": 91, "name": "Pa", "deriv": ["Th"]},
+            {"num": 92, "name": "U",  "deriv": ["Pa"]}]
+#}}}
+
+# dictionnaire numéro --> élément
+# permet de retrouver un élément par son numéro atomique
+NUM_OF = {elt["name"]: elt["num"] for elt in ELEMENTS}
+
+#####################################################
+# CRÉATION DE LA MATRICE DES DÉRIVATIONS D'ÉLÉMENTS #
+#####################################################
+# initialisation
+matrix = [[0 for _ in range(len(ELEMENTS))] for _ in range(len(ELEMENTS))]
+# remplissage
+for elt in ELEMENTS:
+    num = elt["num"]
+    for dv_elt in elt["deriv"]:
+        matrix[num-1][NUM_OF[dv_elt]-1] += 1
+# conversion en tableau numpy
+matrix = np.array(matrix)
+
+# AFFICHER LA MATRICE
+print("Matrice 𝑀 :")
+print("┏", "━"*92, "┓\n┃",
+      "┃\n┃".join([''.join([" 12│12─12┼12"[val + 3*(9==col%10) + 6*(9==ln%10)] for col, val in enumerate(line)]) for ln, line in enumerate(matrix)]),
+      "┃\n┗", "━"*92, "┛",
+      sep="")
+
+# CALCUL DE λ
+eigvals = np.linalg.eigvals(matrix)
+λ = eigvals[np.argmax(np.abs(eigvals))]
+print(f"λ = {np.real(λ)} + {np.imag(λ)}𝑖")
+```
+
+
+<div class="page-break" style="page-break-before: always;"></div>
+
+
+
+
+# Bibliographie et Notes
+
+Cover, T. M., & Gopinath, B. (1987). _Open problems in communication and computation_. Springer-Verlag.
+Ekhad, S. B., & Zeilberger, D. (n.d.). _Proof of Conway’s lost cosmological theorem_. Retrieved [https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf](https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf)
+Lairez, P., & Storozhenko, A. (2025). Conway’s cosmological theorem and automata theory. _The American Mathematical Monthly_, _132_(9), 867–882. [https://doi.org/10.1080/00029890.2025.2549225](https://doi.org/10.1080/00029890.2025.2549225)

ensemble de formules contradictoire.md

@@ -0,0 +1,18 @@
+---
+up:
+  - "[[calcul propositionnel]]"
+tags:
+  - s/maths/logique
+  - o
+aliases:
+  - contradictoire
+---
+
+> [!definition] [[ensemble de formules contradictoire]]
+> Un ensemble de formules $\mathscr{A}$  est **contradictoire** si et seulement si il n'est pas [[ensemble de formules satisfaisable|satisfaisable]]
+^definition
+
+# Propriétés
+
+# Exemples
+

ensemble de formules satisfaisable.md

@@ -0,0 +1,14 @@
+---
+up:
+  - "[[formule logique|formules logiques]]"
+tags:
+  - s/maths/logique
+aliases:
+  - satisfaisable
+---
+
+> [!definition] Définition
+> Soit $\mathscr{A}$ un ensemble de formules du [[calcul propositionnel]]
+> $\mathscr{A}$ est **satisfaisable** (ou **consistant**, ou **non contradictoire**) si et seulement s'il existe au moins une [[valuation]] qui satisfait $\mathscr{A}$
+^definition
+

ensemble de formules satisfait.md

@@ -0,0 +1,21 @@
+---
+up:
+  - "[[calcul propositionnel]]"
+tags:
+  - s/maths/logique
+aliases:
+  - satisfait
+---
+
+> [!definition] [[ensemble de formules satisfait]]
+> Soit $\mathscr{A}$ un ensemble de formules du [[calcul propositionnel]] sur l'ensemble de variables propositionnelles $P$
+> Soit $\delta$ une [[valuation d'une formule logique|valuation]] sur $P$
+> On dit que $\mathscr{A}$ est **satisfait** par $\delta$ si et seulempent si $\delta$ satisfait toutes les formules qui appartiennent à $\mathscr{A}$ :
+> $\boxed{\forall F \in \mathscr{A},\quad \delta(F) = 1}$
+^definition
+
+# Propriétés
+
+# Exemples
+
+

ensemble de formules satisfiable.md

@@ -1,12 +0,0 @@
----
-up:
-  - "[[formule logique|formules logiques]]"
-tags:
-  - s/maths/logique
-aliases:
----
-
-> [!definition] Définition
-> Soit $\mathcal{F}$ l'ensemble des formules propositionnelles
-^definition
-

ensemble.md

@@ -6,9 +6,16 @@ tags:
 aliases:
   - ensembles
 ---
-> [!definition] Définition
-> 
-^definition
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```
+
 
 # Propriétés
 

ensembles de formules logiquement équivalents.md

@@ -0,0 +1,12 @@
+---
+up:
+  - "[[calcul propositionnel]]"
+tags:
+  - s/maths/logique
+aliases:
+  - équivalents
+---
+
+> [!definition] [[ensembles de formules logiquement équivalents]]
+> Deux ensembles de formules $\mathscr{A}$ et $\mathscr{B}$ sont **équivalents** si et seulement si toute formule de $\mathscr{A}$ est conséquence de $\mathscr{B}$ 
+^definition

films.base

@@ -78,7 +78,7 @@ views:
       - property: watchlist
         direction: DESC
     columnSize:
-      file.name: 352
+      file.name: 431
       note.scoreImdb: 47
       note.director: 141
       note.year: 64

filtre de fréchet.md

@@ -6,17 +6,19 @@ tags:
 aliases:
 ---
 
-> [!definition] Définition
-> On définit $\mathscr{F}$ le filtre de Fréchet par : 
+> [!definition] [[filtre de fréchet]]
+> Soit $X$ un ensemble infini.
+> On définit $\mathscr{F}$ le [[filtre]] de Fréchet par : 
 > $A \in \mathscr{F}$ si $X - A$ est fini
+> - i on pourra le noter $\mathscr{F}_{\mathrm{cof}}$
+> 
+> > [!démonstration]- Démonstration que c'est bien un filtre
+> > 1. $X - X = \emptyset$ est bien fini
+> > 2. soient $A, B \in \mathscr{F}$ on a :
+> >    $X - (A \cap B) = (X-A) \cup (X-B)$ 
+> >    or la réunion de deux ensembles finis est finie d'où il suit que $A \cap B \in \mathscr{F}$
+> > 3. Soit $A \in \mathscr{F}$ avec $A \subseteq B$ 
+> >    $X - B \subseteq X - A$ or on sait que $X - A$ est fini, et qu'une partie d'un ensemble fini est finie, d'où on a que $X - B$ est fini et donc que $B \in \mathscr{F}$
 ^definition
 
-# Démonstration que c'est bien un filtre
-
- 1. $X - X = \emptyset$ est bien fini
- 2. soient $A, B \in \mathscr{F}$ on a :
-    $X - (A \cap B) = (X-A) \cup (X-B)$ 
-    or la réunion de deux ensembles finis est finie d'où il suit que $A \cap B \in \mathscr{F}$
- 3. Soit $A \in \mathscr{F}$ avec $A \subseteq B$ 
-    $X - B \subseteq X - A$ or on sait que $X - A$ est fini, et qu'une partie d'un ensemble fini est finie, d'où on a que $X - B$ est fini et donc que $B \in \mathscr{F}$
 

filtre engendré.md

@@ -0,0 +1,21 @@
+---
+up:
+  - "[[filtre]]"
+tags:
+  - s/maths/logique
+aliases:
+---
+
+> [!definition] [[filtre engendré]]
+> Soit $\mathcal{B}$ une [[base de filtre]] sur $X$
+> Le **filtre engendré** par $\mathcal{B}$ est le [[filtre]] $\mathscr{F}_{\mathcal{B}}$ défini par :
+> $\boxed{\mathscr{F}_{\mathcal{B}} = \{ F \in \mathcal{P}(X) \mid \exists B \in \mathcal{B},\quad B \subseteq F \}}$
+> 
+> > [!démonstration]- Démonstration : $\mathscr{F}_{\mathcal{B}}$ est bien un filtre
+> > 
+^definition
+
+# Propriétés
+
+# Exemples
+

firefox troubleshooot.md

@@ -2,10 +2,10 @@
 id: firefox troubleshooot
 aliases: []
 tags:
-  - #t/troubleshoot
+  - 
 up:
   - "[[firefox]]"
-  - "[[firefox troubleshooot]]"
+  - "[[troubleshoot]]"
 ---
 
 ```breadcrumbs

formule conséquence d'un ensemble de formules.md

@@ -0,0 +1,30 @@
+---
+up:
+  - "[[calcul propositionnel]]"
+tags:
+  - s/maths/logique
+aliases:
+  - conséquence
+  - ⊢*
+---
+
+> [!definition] [[formule conséquence d'un ensemble de formules]]
+> Soit $\mathscr{A}$ un ensembles de formules et $G$ une formule du [[calcul propositionnel]]
+> $G$ est **conséquence** de $\mathscr{A}$ si et seulement si toute distribution de valeurs de vérité qui satisfait $\mathscr{A}$ 
+^definition
+
+# Propriétés
+
+> [!proposition]+ 
+> $\mathscr{A} \vdash^{*} G \iff \mathscr{A} \cup \{ \neg G \}$ est [[ensemble de formules contradictoire|contradictoire]]
+> > [!démonstration]- Démonstration
+> > - $\boxed{\implies}$ supposons que $\mathscr{A} \vdash^{*} G$
+> >   Soit $\delta$ une [[valuation]] qui [[ensemble de formules satisfait|satisfait]] $\mathscr{A}$, i.e. $\forall F \in \mathscr{A},\quad \delta(F) = 1$
+> >   Puisque l'on a supposé $\mathscr{A} \vdash^{*} G$ sait que $\delta(G)=1$, et donc que $\delta(\neg G) = 0$, ce qui montre bien qu'aucune valuation satisfaisant $\mathscr{A}$ ne peut satisfaire aussi $\neg G$, et donc que $\mathscr{A} \cup \{ \neg G \}$ est contradictoire
+> > - $\boxed{\impliedby}$ supposons que $\mathscr{A} \cup \{  \neg G \}$ est contradictoire
+> >   Alors, on sait que pour toute valuation $\delta$ on a $\exists F \in \mathscr{A} \cup \{ \neg G \},\quad \delta (F) = 0$
+> > - 
+
+
+# Exemples
+

formule logique close.md

@@ -4,6 +4,7 @@ up:
 tags:
   - s/maths/logique
 aliases:
+  - formule close
 ---
 
 > [!definition] Définition

généralité absolue.md

@@ -42,4 +42,4 @@ critiqué par :
 
 
 ## Obstacle logico-mathématique
-[[paradoxe de Russel]]
+[[paradoxe de Russell]]

homebrew . changing installation settings.md

@@ -0,0 +1,7 @@
+# Changing installation settings
+You can edit settings for a certain app using : 
+`brew edit <name>`
+That opens a configuration file that controls taht installation settings.
+
+Then, you can recompile that app using :
+`brew reinstall --build-from-source <name>`

homebrew . clear cache.md

@@ -0,0 +1,13 @@
+---
+up:
+  - "[[homebrew]]"
+tags:
+  - "#s/informatique"
+aliases:
+  - clear homebrew cache
+---
+
+```sh
+homebrew cleanup --prune=all
+```
+

homebrew . désinstaller.md

@@ -1,10 +1,9 @@
 ---
-alias: [ "homebrew désinstaller avec les dépendances" ]
----
-up:: [[homebrew]]
-title:: "`brew uninstall <package> && brew autoremove`"
-#s/informatique 
-
+up: "[[homebrew]]"
+tags:
+  - "#s/informatique"
+aliases:
+  - homebrew désinstaller avec les dépendances
 ---
 
 Pour désinstaller un package

homebrew.md

@@ -1,13 +1,15 @@
-up::[[installing things]]
-title::"macos package manager"
-#s/informatique
+---
+up: "[[installing things]]"
+tags: 
+  - "#s/informatique"
+---
 
-----
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```
 
-# Changing installation settings
-You can edit settings for a certain app using : 
-`brew edit <name>`
-That opens a configuration file that controls taht installation settings.
-
-Then, you can recompile that app using :
-`brew reinstall --build-from-source <name>`

index.md

@@ -11,5 +11,5 @@ tags: []
 > collapse: true
 > show-attributes: [field]
 > field-groups: [downs]
-> depth: [0, 0]
+> depth: [0, 2]
 > ```

langage des prédicats du premier ordre.md

@@ -0,0 +1,7 @@
+---
+aliases:
+  - langage
+  - 
+up:
+tags:
+---

lauchd.md

@@ -0,0 +1,21 @@
+---
+up:
+  - "[[ligne de commande]]"
+  - "[[système d'exploitation]]"
+tags:
+  - s/informatique
+aliases:
+---
+
+Outil qui gère des daemons.
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```
+
+

launchd.md

@@ -0,0 +1,16 @@
+---
+up:
+tags:
+aliases:
+---
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```
+
+remplace [[cron]] sur macos : permet de schedule des tâches.

limites usuelles.md

@@ -11,6 +11,6 @@ $$\begin{array}{|r|l|}
 \left.\displaystyle\lim_{x\rightarrow+\infty}  \dfrac{e^x}{x^\alpha}\right|_{\alpha>0} & +\infty \\\hline
 \displaystyle\lim_{x\rightarrow+\infty}  & \\\hline
 \left.\displaystyle\lim_{x\rightarrow+\infty} \dfrac{(\ln (x))^{\alpha}}{x^\beta}\right|_{\beta>0} & 0 \\\hline
-\disp\lim_{x\rightarrow 0} \dfrac{\sin x}x & 1\\\hline
-\disp\lim_{x\rightarrow 0} \dfrac{1 - \cos(x)}{x^2} & \dfrac12 \\\hline
+\displaystyle \lim_{x\rightarrow 0} \dfrac{\sin x}x & 1\\\hline
+\displaystyle \lim_{x\rightarrow 0} \dfrac{1 - \cos(x)}{x^2} & \dfrac12 \\\hline
 \end{array}$$

lunchy-go.md

@@ -0,0 +1,28 @@
+---
+up:
+  - "[[terminal commandes]]"
+  - "[[launchd]]"
+tags:
+  - s/informatique
+aliases:
+---
+Wrapper autour de `lauchctl` pour configurer plus aisément [[launchd]].
+- gh https://github.com/sosedoff/lunchy-go
+- source:: [[sosedofflunchy-go OSX Launch Manager]] 
+
+# Installation
+`brew install lunchy-go`
+
+# Cheat sheet
+`lunchy ...`
+- `ls` [pattern]
+- `start` [pattern]
+- `stop` [pattern]
+- `restart` [pattern]
+- `status`, `ps` [pattern]
+- `install` [file]
+- `show` [pattern]
+- `edit` [pattern]
+- `remove`, `rm` [pattern]
+- `scan` [path]
+

macos system data.md

@@ -0,0 +1,10 @@
+---
+up:
+  - "[[troubleshoot]]"
+  - "[[macos]]"
+tags:
+  - "#s/informatique"
+aliases:
+---
+
+problème : beaucoup de place perdue dans "system data"

modèle.md

@@ -1,9 +0,0 @@
-#s/maths/logique
-
-----
-
-Un modèle logique est  **une [[interprétation]] particulière d'une [[proposition]]**.
-
-On dit qu'une interprétation $I$ est un [[modèle]] d'une [[proposition]] logique $\Phi$ ssi $I(\Phi) = \mathbb{V}$.
-
-Si toutes les interprétations de $P$ sont aussi des modèles de $P$, alors on dit que $P$ est une [[tautologie]].

norme p.md

@@ -1,12 +1,11 @@
 ---
-id: norme p
+up: "[[distances particulières]]"
 aliases:
   - norme de Hölder
   - normes p
-tags: []
+tags:
+  - "#s/maths/algèbre"
 ---
-up:: [[distances particulières]]
-#s/maths/algèbre 
 
 > [!definition] norme $p$ - définition sur $\mathbb{R}^{n}$
 > On définit sur $\mathbb{R}^{n}$ la norme $\|\cdot \|_{p}$ :

notes sur l'éthique de spinoza.md

@@ -292,480 +292,478 @@ e9894d7bda60af851e0fb13a19aa0e8095919e3e: [[attachments/Pasted Image 20260221211
 
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-
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 ```
 %%

personnalités autoritaires.md

@@ -21,4 +21,6 @@ up:: [[politique]], [[psychologie]], [[sociologie]]
 - projectivité
     - projection à l'extérieur de pulsions émotionnelles intérieures
 - sexe
-    - intérêt exagéré pour les "affaires sexuelles"
+    - intérêt exagéré pour les "affaires sexuelles"
+
+ 

phrases.md

@@ -2,84 +2,84 @@
 
 
 # Claire
-> - j'ai un truc qui bloque le levier de vitesse
-> - ça s'appelle du maquillage !
+- j'ai un truc qui bloque le levier de vitesse
+- ça s'appelle du maquillage !
 
-> - Ah, c'est pas toi qui est sous la douche !
-> - ah bon ?
+- Ah, c'est pas toi qui est sous la douche !
+- ah bon ?
 
- - je suis malade, j'ai du mal à ne plus l'être
+- je suis malade, j'ai du mal à ne plus l'être
 
 # Oscar
- - "Dans mon contrôle de maths, pour avoir $20$, il fallait avoir $0$"
- - Tu as entendu, Oscar ? Gérard a dit que tu avais des parents intelligents ! Et Oscar de répondre : « s’il a fallu quelqu’un d’aussi intelligent que lui pour le remarquer, c’est que c’était pas facile à voir ! »
- - "qui à fait l'appel du 18 juin ? Je sait pas, mais il devait pas être bien après 18 joints"
- - "il à perdu sa clef !", "bah non, c'est à Paris, Saclay !"
- - c'est pas parce que tu vas plus vite que le son que tu est dans le silence
+- "Dans mon contrôle de maths, pour avoir $20$, il fallait avoir $0$"
+- Tu as entendu, Oscar ? Gérard a dit que tu avais des parents intelligents ! Et Oscar de répondre : « s’il a fallu quelqu’un d’aussi intelligent que lui pour le remarquer, c’est que c’était pas facile à voir ! »
+- "qui à fait l'appel du 18 juin ? Je sait pas, mais il devait pas être bien après 18 joints"
+- "il à perdu sa clef !", "bah non, c'est à Paris, Saclay !"
+- c'est pas parce que tu vas plus vite que le son que tu est dans le silence
 
 # Clara
- - Je me pose des questions sur pourquoi les gens sont si stupides
+- Je me pose des questions sur pourquoi les gens sont si stupides
 
 # Samuel
- - Pourquoi les plongeurs basculent en arrière ? Parce que si ils basculent en avant, ils tombent dans le bateau.
+- Pourquoi les plongeurs basculent en arrière ? Parce que si ils basculent en avant, ils tombent dans le bateau.
 
 # Jean Claude
- - "Le dimanche il pleut plus souvent à l'extérieur"
+- "Le dimanche il pleut plus souvent à l'extérieur"
 
 # Gérard
- - "Le 3$^{\text{ème}}$ degré est un premier non avoué"
+- "Le 3$^{\text{ème}}$ degré est un premier non avoué"
 # Chambert-loir
- - "j'ai qu'une envie c'est que le cours soit fini comme ça j'ai pas à faire la preuve"
+- "j'ai qu'une envie c'est que le cours soit fini comme ça j'ai pas à faire la preuve"
 
 # Autres
- - M. Labroche
-     - "Si vous voulez parler en cours, c'est simple : Master, Doctorat, Concours de prof, et vous avez le droit de parler en cours !"
-     - Il ne veut pas lâcher le bord de la piscine, sauf que là c'est pas une piscine, c'est un pédiluve
-     - à chaque fois que je dis des conneries, c'est du CO2 pour rien
-     - "je n'oscille pas infiniment entre l'ennui et la souffrance", "c'est parce que tu as ton ordi qui arive à se connecter"
- - Evelyne Moreau
-     - "Ca converge vers $+\infty$"
-     - "le voisinage de $+\infty$, on y va pas souvent"
- - "l'ordre, ça à du sens"
- - "c'est ma grand-mère maternelle du côté de mon père"
- - "je ne vous fait pas la bise, j'ai les mains mouillées"
- - Felix John
-     - "I'd rather just bring a pillow" ("you don't have to suffer, just bring a pillow !")
- - Barbara
-     - la mort, c'est pas très bon pour la santé
- - Max Lemoine
-     - "je sais écrire mon prénom en anglais"
- - "ta tête, elle te va bien !"
- - Dario Weinberger
-     - "Mais non, c'est juste que je suis né avant les autres"
- - Catherine :
-     - c'est un prof : ça s'apprivoise sinon ça mord
-     - Tours c'est vraiment une boulangerie
- - Damien Roverselli
-     - quand on voit des mains dans les grottes, ont appelle ça de la peinture, donc un coup de poing, ça peut être de l'art
- - Maxence Flavier
-     - Si t'as trop froid c'est que c'est pas assez chaud
-     - Je veux conduire, mais je louche
- - Claudette Louchart
-     - "Je vais dire un truc, je sait que ça sert à rien, mais je vais le dire quand même"
- - E. Escriva et J. Aligon
-     - Un "sex" de 0.051 ne signifie rien, un IMC de -0.03 n'a aucun sens médical
- - Hichem
-     - "est-ce que j'ai la force de faire l'exercice 3 ?", regarde l'exercice, et 30s plus tard : "bon, on va faire l'exercice 7"
-     - discussion :
-         - "t'as compris ?" (Hichem)
-         - "non." (un étudiant)
-         - "bah alors viens au tableau."
- - L'équation d'une corde vibrante tient compte du fait que les extrémités sont fixes. Pour les guitaristes, je ne sais pas si vous avez remarqué, mais quand la corde pète, le son est nettement moins joli.
- - les inégalités, il n'y a rien de plus traître
- - C'est dangeureux d'appeller $U$ une réunion
- - l'ordre de $x^{k}$ c'est $d$ 
- - parfois il me faut 2 ou 3 jours pour savoir si c'est évident ou pas
- - d'aussi loin que je me souvienne, j'ai toujours vécu perso (BanHammer - discord Chez MrPhi)
- - Bertrand Gentou (prof d'algorithmique)
-     - on dépile, on visite, on empile et on dépile les enfants
-     - je peux l'éliminer, il a pas d'enfants, c'est bon
- - c'est pas fait pour être agréable, les machines de Turing
+- M. Labroche
+    - "Si vous voulez parler en cours, c'est simple : Master, Doctorat, Concours de prof, et vous avez le droit de parler en cours !"
+    - Il ne veut pas lâcher le bord de la piscine, sauf que là c'est pas une piscine, c'est un pédiluve
+    - à chaque fois que je dis des conneries, c'est du CO2 pour rien
+    - "je n'oscille pas infiniment entre l'ennui et la souffrance", "c'est parce que tu as ton ordi qui arive à se connecter"
+- Evelyne Moreau
+    - "Ca converge vers $+\infty$"
+    - "le voisinage de $+\infty$, on y va pas souvent"
+- "l'ordre, ça à du sens"
+- "c'est ma grand-mère maternelle du côté de mon père"
+- "je ne vous fait pas la bise, j'ai les mains mouillées"
+- Felix John
+    - "I'd rather just bring a pillow" ("you don't have to suffer, just bring a pillow !")
+- Barbara
+    - la mort, c'est pas très bon pour la santé
+- Max Lemoine
+    - "je sais écrire mon prénom en anglais"
+- "ta tête, elle te va bien !"
+- Dario Weinberger
+    - "Mais non, c'est juste que je suis né avant les autres"
+- Catherine :
+    - c'est un prof : ça s'apprivoise sinon ça mord
+    - Tours c'est vraiment une boulangerie
+- Damien Roverselli
+    - quand on voit des mains dans les grottes, ont appelle ça de la peinture, donc un coup de poing, ça peut être de l'art
+- Maxence Flavier
+    - Si t'as trop froid c'est que c'est pas assez chaud
+    - Je veux conduire, mais je louche
+- Claudette Louchart
+    - "Je vais dire un truc, je sait que ça sert à rien, mais je vais le dire quand même"
+- E. Escriva et J. Aligon
+    - Un "sex" de 0.051 ne signifie rien, un IMC de -0.03 n'a aucun sens médical
+- Hichem
+    - "est-ce que j'ai la force de faire l'exercice 3 ?", regarde l'exercice, et 30s plus tard : "bon, on va faire l'exercice 7"
+    - discussion :
+        - "t'as compris ?" (Hichem)
+        - "non." (un étudiant)
+        - "bah alors viens au tableau."
+- L'équation d'une corde vibrante tient compte du fait que les extrémités sont fixes. Pour les guitaristes, je ne sais pas si vous avez remarqué, mais quand la corde pète, le son est nettement moins joli.
+- les inégalités, il n'y a rien de plus traître
+- C'est dangeureux d'appeller $U$ une réunion
+- l'ordre de $x^{k}$ c'est $d$ 
+- parfois il me faut 2 ou 3 jours pour savoir si c'est évident ou pas
+- d'aussi loin que je me souvienne, j'ai toujours vécu perso (BanHammer - discord Chez MrPhi)
+- Bertrand Gentou (prof d'algorithmique)
+    - on dépile, on visite, on empile et on dépile les enfants
+    - je peux l'éliminer, il a pas d'enfants, c'est bon
+- c'est pas fait pour être agréable, les machines de Turing
 
 
 

projets persos.md

@@ -0,0 +1,12 @@
+---
+up:
+tags:
+aliases:
+---
+
+> [!todo] Projets non-commencés
+> ```dataview
+> LIST title
+> FROM ""
+> WHERE econtains(up, this.file.link)
+> ```

raisonnement valide.md

@@ -5,4 +5,4 @@ Un raisonnement est dit _valide_ ssi sa conclusion est la conséquence logique d
 
 # Notation
 $$P1, \ldots, Pn \models B$$
-Le raisonnement Est valide ssi $B$ est bien [[modèle|modélisé]] par $P1,\ldots,Pn$.
+Le raisonnement Est valide ssi $B$ est bien [[théorie des modèles . modèle|modélisé]] par $P1,\ldots,Pn$.

relation d'ordre.md

@@ -1,6 +1,7 @@
 ---
-up:: [[relation]]
-#s/maths/algèbre 
+up: "[[relation]]"
+tags:
+  - "#s/maths/algèbre"
 ---
 
 > [!definition] Relation d'ordre

satisfaisable.md

@@ -1,7 +1,7 @@
 #s/maths/logique
 
 ----
-Une [[proposition]] est _satisfaisable_ si elle admet **au moins un [[modèle]]**.
+Une [[proposition]] est _satisfaisable_ si elle admet **au moins un [[théorie des modèles . modèle]]**.
 
 Une [[proposition]] qui n'est pas satisfaisable est une [[contradiction]]
 

sources/clippings/OV Klok.md

@@ -0,0 +1,16 @@
+---
+link: "https://jplattel.nl/project/ov-klok/"
+author:
+published: 2024-02-14
+created: 2026-05-31
+description: "I’m Joost Plattel, I'd like to call myself an auxiliary technologist. I assist organisations and individuals with technology and help them future strategies."
+tags:
+  - "t/clippings"
+---
+The [OV Klok](https://ovklok.nl/) is a small hardware project that show the time left before the next departure of public transport you use. It’s made with and ESP32 module and 7 segment digit display.
+
+![](https://jplattel.nl/img/ovklok.jpeg)
+
+You can [order one](https://shop.ovklok.nl/) if you live in the Netherlands and use public transport a lot from a specific location. The enclosure is made by pressure-forming plastic in the [Mayku Multiplier](https://mayku.me/multiplier) and a 3D print allowing for different methods of mounting and freestanding use.
+
+The ESP32 runs on Circuit Python and is fully configurable with a USB-C cable through the browser with the use of WebSerial. This skips troublesome setups like captive portals or file editing. It’s a simple and calm device allowing you to catch your public transport right on time!

sources/clippings/github/citeorder Simple command-line tool to relabel Footnotes in Markdown files in numerical order..md

@@ -0,0 +1,173 @@
+---
+link: https://github.com/dhanushka2001/citeorder
+created: 2026-05-11
+tags:
+  - "#t/clippings/github"
+  - s/informatique
+---
+[![Logo](https://github.com/user-attachments/assets/43f400c2-ba67-45a9-b196-53757bf9931b#gh-dark-mode-only)](https://github.com/user-attachments/assets/43f400c2-ba67-45a9-b196-53757bf9931b#gh-dark-mode-only)
+
+Simple command-line tool to correctly reorder Footnotes in Markdown files.
+
+> [!tip] Tip
+> For those who don't wish to use the command-line, I have made a [Chrome Extension](https://github.com/dhanushka2001/citeorder-github) which adds a toolbar inside GitHub's README.md text editor with a button to reorder footnotes.
+
+## Motivation
+
+Markdown processors that support footnotes (e.g. [GitHub’s Markdown engine](https://github.com/github/cmark-gfm), which implements the [GitHub Flavored Markdown](https://github.github.com/gfm) spec) automatically reorder footnotes when converting `.md` files to HTML. However, `citeorder` fixes the ordering in the `.md` file itself, making it neater and easier to manage lots of footnotes. Especially useful when needing to add new footnotes in the middle of a long `.md` file and not having to spend ages reordering every in-text and full-entry footnote manually (🥲).
+
+In-text footnotes (`"Alice here",[^1]`) and full-entry footnotes (`[^1]: Alice`) are a many-to-one relationship. `citeorder` assumes the connections are correct, and relabels them according to the order in which the **in-text footnotes** appear.
+
+## How to use
+
+1. Download the precompiled executable from the latest [release](https://github.com/dhanushka2001/citeorder/releases).
+	Installation via [Homebrew](https://github.com/dhanushka2001/homebrew-citeorder) (macOS/Ubuntu):
+	```
+	brew install dhanushka2001/citeorder/citeorder
+	```
+	Installation via the [AUR](https://aur.archlinux.org/packages/citeorder) (Arch):
+	```
+	yay -S citeorder
+	```
+	Or clone the repo and compile source code
+	If you want to compile the source code yourself, clone the repo and compile `citeorder.c`:
+	```
+	git clone https://github.com/dhanushka2001/citeorder
+	```
+	```
+	gcc -Wall -O2 citeorder.c -o citeorder
+	```
+2. To run, simply enter into the terminal:
+	```
+	citeorder input.md
+	```
+	where `input.md` is the Markdown file whose Footnotes you want reordered. `citeorder` will keep the original file as is and output the changes to a new file, `input-fixed.md`.
+	To allow relaxed quote handling, do:
+	```
+	citeorder -q input.md
+	```
+	For more info and options, run:
+	```
+	citeorder -h
+	```
+
+## Example
+
+`example.md`:
+
+```
+"Alice says hi".[^1]
+
+[^1]: Alice
+
+"Bob is here".[^7] "I'm Charlie",[^4] "Daniel!",[^5] here.
+
+[^4]: Charlie
+[^3]: Gary
+[^5]: Daniel
+[^7]: Bob
+
+Is "Ethan"[^8] here?
+
+[^8]: Ethan
+
+"Bob and Charlie here again"[^7][^4]
+
+[^6]: Fred
+```
+
+Running:
+
+```
+citeorder example.md
+```
+
+will produce `example-fixed.md`:
+
+```
+"Alice says hi".[^1]
+
+[^1]: Alice
+
+"Bob is here".[^2] "I'm Charlie",[^3] "Daniel!",[^4] here.
+
+[^2]: Bob
+[^3]: Charlie
+[^4]: Daniel
+[^6]: Gary
+
+Is "Ethan"[^5] here?
+
+[^5]: Ethan
+
+"Bob and Charlie here again"[^2][^3]
+
+[^7]: Fred
+```
+
+## Cases handled
+
+- No changes needed.
+- Stacked in-text footnotes, e.g. `"hello",[^3][^1][^5]` → `"hello",[^1][^2][^3]`.
+- Single punctuation (or none) after end quote, e.g. `"A"[^3] "B",[^2] "C".[^6] "D"![^5]` → `"A"[^1] "B",[^2] "C".[^3] "D"![^4]`.
+- Improper quote, e.g. `"hello[^1]`, `"hello",,[^1]`, `hello"[^1]`, `"hello" [^1]` produces an error message like: `ERROR: in-text citation [^1] not properly quoted (line 5)`. Can ignore this error with the `-q` / `--relaxed-quotes` flag.
+- Full-entry footnotes with no matching in-text footnotes simply get bubbled to the end of the ordering.
+- In-text footnotes with no matching full-entry footnote produce an error message like: `ERROR: in-text citation [^2] without full-entry (line 3)`.
+- Duplicate full-entry footnotes, e.g.
+	```
+	[^4]: Alice
+	[^4]: Bob
+	```
+	produces an error message like: `ERROR: duplicate [^4] full-entry citations (line 7 and 8)`.
+- Footnotes inside inline code (`"A"[^1]`) and fenced code blocks:
+	```
+	"A"[^1]
+	[^1]: A
+	[^2]: B
+	```
+	are ignored.
+- Footnote labels with letters/symbols are supported, and will be relabeled accordingly, e.g. `"A"[^6b]` → `"A"[^1]`.
+- Spaces in the in-text or full-entry footnotes. Spaces outside the label for in-text footnotes, e.g. `"A"[^  Alice ]` are accepted by Markdown processors, and `citeorder` will convert that to `"A"[^1]`. However, for full-entry footnotes, e.g. `[^ 4b  ]: Alice`, it is not accepted, and in `citeorder` it will produce an error message like: `ERROR: [^ 4b  ] full-entry citation contains a space (line 3)`. For both in-text and full-entry footnotes, spaces **in** the label itself, e.g. `"A"[^4 b]`, `[^4 b]: Alice`, are not accepted, and in `citeorder` you will get an error message.
+- In-text or full-entry footnote missing a label, e.g. `"A"[^]`, will produce an error message like: `ERROR: in-text citation [^] missing label (line 7)`.
+- Multiline quote:
+	```
+	"T"[^4]
+	"This quote takes
+	up multiple lines
+	but is still valid",[^3]
+	"H",[^6]
+	[^4]: T
+	[^6]: H
+	[^3]: Multiline quote
+	```
+	becomes:
+	```
+	"T"[^1]
+	"This quote takes
+	up multiple lines
+	but is still valid",[^2]
+	"H",[^3]
+	[^1]: T
+	[^2]: Multiline quote
+	[^3]: H
+	```
+- Duplicate full-entry footnotes, e.g.
+	```
+	"A"[^dupe], "B"[^dupe]
+	[^dupe]: A
+	[^dupe]: B
+	"C"[^dupe]
+	[^dupe]: C
+	"D"[^1]
+	[^1]: D
+	```
+	can be auto-incremented using the `-d` / `--relaxed-duplicates` flag (must be only ONE duplicate footnote label, and must have an equal number of full-entry and in-text duplicates):
+	```
+	"A"[^1], "B"[^2]
+	[^1]: A
+	[^2]: B
+	"C"[^3]
+	[^3]: C
+	"D"[^4]
+	[^4]: D
+	```

sources/clippings/github/sosedofflunchy-go OSX Launch Manager.md

@@ -0,0 +1,161 @@
+---
+link: "https://github.com/sosedoff/lunchy-go"
+created: 2026-06-05
+tags:
+  - "#t/clippings/github"
+---
+## lunchy-go
+
+A friendly wrapper for launchctl. Start your agents and go to lunch!
+
+This is a port of original [lunchy](https://github.com/mperham/lunchy) ruby gem by Mike Perham with extra functionality.
+
+## Overview
+
+Don't you hate OSX's launchctl? You have to give it exact filenames. The syntax is annoying different from Linux's nice, simple init system and overly verbose. It's just not a very developer-friendly tool.
+
+Lunchy aims to be that friendly tool by wrapping launchctl and providing a few simple operations that you perform all the time:
+
+- ls \[pattern\]
+- start \[pattern\]
+- stop \[pattern\]
+- restart \[pattern\]
+- status, ps \[pattern\]
+- install \[file\]
+- show \[pattern\]
+- edit \[pattern\]
+- remove, rm \[pattern\]
+- scan \[path\]
+
+where pattern is just a substring that matches the agent's plist filename.
+
+So instead of:
+
+```
+$ launchctl load ~/Library/LaunchAgents/io.redis.redis-server.plist
+```
+
+you can do this:
+
+```
+$ lunchy start redis
+```
+
+and:
+
+```
+$ lunchy ls
+
+com.danga.memcached
+com.google.keystone.agent
+com.mysql.mysqld
+io.redis.redis-server
+org.mongodb.mongod
+```
+
+## Install
+
+You can install binary by running the following bash command:
+
+```
+curl -s https://raw.githubusercontent.com/sosedoff/lunchy-go/master/install.sh | bash
+```
+
+#### Homebrew
+
+Install using [Homebrew](https://brew.sh/):
+
+```
+brew install lunchy-go
+```
+
+#### Binary Releases
+
+Precompiled binaries are available on Github: [https://github.com/sosedoff/lunchy-go/releases](https://github.com/sosedoff/lunchy-go/releases)
+
+#### Build from source
+
+Build source code with Go 1.2+:
+
+```
+git clone https://github.com/sosedoff/lunchy-go.git $GOPATH/src/lunchy
+cd lunchy
+go build
+mv ./lunchy-go /usr/local/bin/lunchy
+```
+
+## Usage
+
+Add a new plist:
+
+```
+# Install plist
+$ lunchy install /usr/local/Cellar/redis/2.8.1/homebrew.mxcl.redis.plist
+```
+
+Manage services:
+
+```
+$ lunchy start redis
+$ lunchy stop redis
+$ lunchy restart redis
+$ lunchy status redis
+```
+
+If you have multiple plists from homebrew, you can simple control all of them:
+
+```
+$ lunchy status
+homebrew.mxcl.elasticsearch
+homebrew.mxcl.mysql
+homebrew.mxcl.postgresql
+homebrew.mxcl.redis
+
+# Will stop all processes prefixed by "homebrew"
+$ lunchy stop homebrew
+```
+
+Manage plists:
+
+```
+$ lunchy show redis
+$ lunchy edit redis
+```
+
+Scan directory for existing plists:
+
+```
+$ lunchy scan /usr/local/Cellar
+```
+
+Scan all homebrew plists:
+
+```
+$ lunchy scan homebrew
+```
+
+## Profiles
+
+When switching between different projects you might find yourself stopping and starting lots of different daemons in order to reduce memory usage. This is all good but there's a better way of doing it. Enter lunchy profiles.
+
+Profile file `.lunchy` should be placed under your project's root directory and include a list of services that needs to be started or stopped. Example:
+
+```
+postgres
+redis
+elasticsearch
+```
+
+Then you can simply run the following command to start/stop/restart ALL of them at once:
+
+```
+lunchy start
+lunchy stop
+lunchy restart
+```
+
+## License
+
+The MIT License (MIT)
+
+Copyright (c) 2013-2015 Dan Sosedoff, [dan.sosedoff@gmail.com](mailto:dan.sosedoff@gmail.com)

sources/films/Ah-ga-ssi.md

@@ -0,0 +1,29 @@
+---
+genre:
+  - "[[Drame]]"
+  - "[[Romantique]]"
+  - "[[Thriller]]"
+director:
+  - "[[Park Chan-wook]]"
+rating:
+scoreImdb: 8.1
+cast:
+  - "[[Kim Min-hee]]"
+  - "[[Ha Jung-woo]]"
+  - "[[Cho Jin-woong]]"
+cover: "https://m.media-amazon.com/images/M/MV5BMTE5MDAyZjMtYjNhMi00YTE3LThhNjgtNTNiNWZhNzVkNjFkXkEyXkFqcGc@._V1_.jpg"
+plot: "Une femme est embauchée en tant que servante d'une héritière japonaise, mais elle est secrètement impliquée dans un complot visant à l'escroquer."
+year: 2016
+created: 2026-05-25
+tags:
+  - "t/source/film"
+  - "s/art/cinema"
+nb_times_seen: "0"
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/films/Bakjwi.md

@@ -0,0 +1,29 @@
+---
+genre:
+  - "[[Drame]]"
+  - "[[Fantastique]]"
+  - "[[Horreur]]"
+director:
+  - "[[Park Chan-wook]]"
+rating:
+scoreImdb: 7.1
+cast:
+  - "[[Song Kang-ho]]"
+  - "[[Kim Ok-bin]]"
+  - "[[Choi Hee-jin]]"
+cover: "https://m.media-amazon.com/images/M/MV5BMDIxMTk2MjAtYTgzNy00NDE5LTg2MWQtYjM5ODBhODZkN2M4XkEyXkFqcGc@._V1_.jpg"
+plot: "A la suite d'une expérience médicale ratée, un prêtre devient un vampire. Sa vie ascétique change du tout au tout."
+year: 2009
+created: 2026-05-25
+tags:
+  - "t/source/film"
+  - "s/art/cinema"
+nb_times_seen: "0"
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/films/Certains l'aiment chaud - Some Like It Hot IMDb.md

@@ -0,0 +1,22 @@
+---
+genre:
+director:
+rating:
+scoreImdb:
+cast:
+cover:
+plot: Trailer for the classic comedy Some Like It Hot, starring Tony Curtis, Jack Lemmon, and Marilyn Monroe
+year: 1959
+created: 2026-05-25
+tags:
+  - t/source/film
+  - s/art/cinema
+nb_times_seen: "0"
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/films/Goemool.md

@@ -0,0 +1,29 @@
+---
+genre:
+  - "[[Drame]]"
+  - "[[Horreur]]"
+  - "[[Science-fiction]]"
+director:
+  - "[[Bong Joon Ho]]"
+rating:
+scoreImdb: 7.1
+cast:
+  - "[[Song Kang-ho]]"
+  - "[[Byun Hee-Bong]]"
+  - "[[Park Hae-il]]"
+cover: "https://m.media-amazon.com/images/M/MV5BOGY1ZDcyNTQtOTdkMy00NzY0LThiM2ItNzM4ZmNhZmQzOGU0XkEyXkFqcGc@._V1_.jpg"
+plot: "Un monstre émerge du fleuve Han à Séoul et se met à attaquer la foule. La famille aimante d'une victime fait tout son possible pour la sauver des griffes de la créature."
+year: 2006
+created: 2026-05-25
+tags:
+  - "t/source/film"
+  - "s/art/cinema"
+nb_times_seen: "0"
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/films/Jim Queen.md

@@ -0,0 +1,30 @@
+---
+genre:
+  - "[[Animation]]"
+  - "[[Aventure]]"
+  - "[[Comédie]]"
+director:
+  - "[[Nicolas Athane]]"
+  - "[[Marco Nguyen]]"
+rating:
+scoreImdb: 6.8
+cast:
+  - "[[François Sagat]]"
+  - "[[Jérémy Gillet]]"
+  - "[[Philippe Katerine]]"
+cover: https://m.media-amazon.com/images/M/MV5BOWY2MTE5NDUtOGExNC00MTQwLTg3NTAtZmQ3ZDUwZjYwYzkzXkEyXkFqcGc@._V1_.jpg
+plot: Jim, icône sexy de la scène gay parisienne, voit sa vie basculer lorsqu'il contracte l'Hétérose, un étrange virus qui transforme les hommes gays en hétérosexuels .
+year: 2026
+created: 2026-05-25
+tags:
+  - t/source/film
+  - s/art/cinema
+nb_times_seen: 0
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/films/The Man from Earth.md

@@ -0,0 +1,29 @@
+---
+genre:
+  - "[[Drame]]"
+  - "[[Fantastique]]"
+  - "[[Mystère]]"
+director:
+  - "[[Richard Schenkman]]"
+rating:
+scoreImdb: 7.8
+cast:
+  - "[[David Lee Smith]]"
+  - "[[Tony Todd]]"
+  - "[[John Billingsley]]"
+cover: "https://m.media-amazon.com/images/M/MV5BOTE1NGYxNjgtYmVlMS00ODEwLTg2NjAtMTdjODMzY2I1ZjZmXkEyXkFqcGc@._V1_.jpg"
+plot: "Une fête d'au revoir impromptue pour le Professeur John Oldman se transforme en interrogatoire mystérieux après que l'universitaire sur le départ révèle à ses collègues un passé plus étrange qu'ils n'auraient pu s'imaginer."
+year: 2007
+created: 2026-05-26
+tags:
+  - "t/source/film"
+  - "s/art/cinema"
+nb_times_seen: "0"
+date_last_seen:
+---
+
+`VIEW[Vu {nb_times_seen} fois (le {date_last_seen})][text]`
+`BUTTON[film_update_date_last_seen]` `BUTTON[film_jamais_vu]`
+
+- score`VIEW[IMDB : {scoreImdb}/10][text]`
+- Note personnelle : `INPUT[slider(addLabels, minValue(0), maxValue(10), defaultValue(5)):rating]` `VIEW[{rating}/10][text]`

sources/zotero/bibliographie/biblio.bib

@@ -511,6 +511,27 @@
   file = {/Users/oscarplaisant/Zotero/storage/767E3XLT/what-is-functional-programming.html}
 }
 
+@article{lairezConwaysCosmologicalTheorem2025,
+  title = {Conway's Cosmological Theorem and Automata Theory},
+  author = {Lairez, Pierre and Storozhenko, Aleksandr},
+  date = {2025-10-21},
+  journaltitle = {The American Mathematical Monthly},
+  shortjournal = {The American Mathematical Monthly},
+  volume = {132},
+  number = {9},
+  eprint = {2409.20341},
+  eprinttype = {arXiv},
+  eprintclass = {cs},
+  pages = {867--882},
+  issn = {0002-9890, 1930-0972},
+  doi = {10.1080/00029890.2025.2549225},
+  url = {http://arxiv.org/abs/2409.20341},
+  urldate = {2026-05-02},
+  abstract = {John Conway proved that every audioactive sequence (a.k.a. look-and-say) decays into a compound of 94\textasciitilde elements, a statement he termed the cosmological theorem. The underlying audioactive process can be modeled by a finite-state machine, mapping one sequence of integers to another. Leveraging automata theory, we propose a new proof of Conway's theorem based on a few simple machines, using a computer to compose and minimize them.},
+  keywords = {Computer Science - Formal Languages and Automata Theory},
+  file = {/Users/oscarplaisant/Zotero/storage/8MAWWH76/Lairez and Storozhenko - 2025 - Conway's cosmological theorem and automata theory.pdf;/Users/oscarplaisant/Zotero/storage/JF782S4T/2409.html}
+}
+
 @article{linEffectsWhiteNoise2022,
   title = {The {{Effects}} of {{White Noise}} on {{Attentional Performance}} and {{On-Task Behaviors}} in {{Preschoolers}} with {{ADHD}}},
   author = {Lin, Hung-Yu},
@@ -625,11 +646,13 @@
   file = {/Users/oscarplaisant/Zotero/storage/42P5K7TK/Okasaki - 1999 - Purely Functional Data Structures.pdf}
 }
 
-@online{OpenProblemsCommunication,
-  title = {Open Problems in Communication and Computation - {{Anna}}’s {{Archive}}},
-  url = {https://annas-archive.gd/md5/47f7db963973665771542f4578a8302f},
-  urldate = {2026-03-27},
-  file = {/Users/oscarplaisant/Zotero/storage/822E4RYV/47f7db963973665771542f4578a8302f.html}
+@book{OpenProblemsCommunication1987,
+  title = {Open Problems in Communication and Computation},
+  author = {Cover, Thomas M. and Gopinath, B.},
+  date = {1987-10},
+  publisher = {Springer-Verlag},
+  location = {Berlin, Heidelberg},
+  isbn = {978-0-387-96621-2}
 }
 
 @inreference{ParadigmeProgrammation2023,
@@ -833,3 +856,10 @@
   keywords = {communication,modèle,paradigme,schéma,théorie},
   file = {/Users/oscarplaisant/Zotero/storage/LFD49R3K/Willett - 1996 - Paradigme, théorie, modèle, schéma  qu’est-ce donc .pdf}
 }
+
+@article{ZeilbergerDoronCosmologicalTheorem,
+  title = {Proof of {{Conway}}'s Lost Cosmological Theorem},
+  author = {Ekhad, Shalosh B. and Zeilberger, Doron},
+  url = {https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/horton.pdf},
+  file = {/Users/oscarplaisant/Zotero/storage/NDV3AFE4/horton.pdf}
+}

théorie des ensemble NBC.md

@@ -0,0 +1,187 @@
+---
+up:
+  - "[[ensemble]]"
+tags:
+  - s/maths/logique
+aliases:
+---
+Cette théorie ne se base pas sur des ensembles directement, mais sur des **classes**.
+Les classes sont caractérisées par $\in$, autrement dit une classe est définie par le prédicat indiquant ce qu'elle contient.
+
+# Définitions et Axiomes
+> [!definition] Classe
+> Une classe $C$ est un objet caractérisé par sa relation d'appartenance, c'est-à-dire que pour tout objet $x$ on pourra dire si $x \in C$ ou non.
+^def-classe
+
+> [!proposition]+ Axiome d'extentionnalité
+> Deux choses contenant les mêmes éléments sont égales.
+> Autrement dit, $C_1 = C_2$ si et seulement si $\forall x,\quad x \in C_1 \iff x \in C_2$
+^ax-extentionnalite
+
+> [!definition] Inclusion
+> La relation d'inclusion, notée $\subseteq$ est définie par :
+> $C_1 \subseteq C_2 \iff \text{pour toute classe } X \text{ avec } X \in C_1 \text{ on a } X\in C_2$
+^def-inclusion
+
+> [!definition] Ensemble
+> Une classe $A$ est un **ensemble** s'il existe une classe $C$ telle que $A \in C$.
+> - i l'axiome d'extentionnalité s'applique également sur les ensembles
+> - i on note $\mathcal{M}$ le prédicat "est un ensemble" ($\mathcal{M}(x) \iff x \text{ est un ensemble}$)
+^def-ensemble
+
+> [!definition] Union et Intersection
+> Soient $C_1$ et $C_2$ deux classes
+> - $C_1 \cup C_2$ est une classe dont les éléments sont les $X$ qui appartiennent à $C_1$ ou à $C_2$
+> - $C_1 \cap C_2$ est une classe dont les éléments sont les $X$ qui appartiennent à $C_1$ et à $C_2$
+> - i on sait par l'axiome d'extentionnalité que $C_1 \cup C_2$ et $C_1 \cap C_2$ sont uniquement déterminés par ces définitions
+^def-union-intersection
+
+> [!definition] Complémentaire
+> Soit $C$ une classe
+> $C^{\complement}$ est la classe qui a pour éléments les $X$ tels que $X \notin C$
+> - i on sait par l'axiome d'extentionnalité que $C^{\complement}$ est uniquement déterminé par ces définitions
+>   
+^def-complementaire 
+
+> [!proposition]+ Axiome d'intersection
+> Si $x$ est un ensemble, si $C$ est une classe, alors $x \cap C$ est un ensemble
+> - i Par conséquence, si une classe $C$ est contenue dans un ensemble $A$, alors $C$ est un ensemble aussi.
+>     - dem car $C \subseteq A$ entraine $C = C \cap A$
+^ax-intersection
+
+> [!proposition]+ Axiome de la paire
+> Si $x$ et $y$ sont des ensemble, alors il existe un ensemble dont les seuls éléments sont $x$ et $y$.
+> $\tiny\mathcal{M}(x) \wedge \mathcal{M}(y) \implies (\exists z,\quad \mathcal{M}(z) \wedge x \in z \wedge y \in z \wedge (\forall t,\quad t \in z \implies (t=x \vee t=z)))$
+> - i par l'axiome d'extentionnalité, on sait qu'il n'existe qu'un seul tel ensemble, que l'on note $\{ x, y \}$
+> - i si $x = y$ on note simplement $\{ x \}$, c'est un **singleton**
+> 
+> > [!proposition]+ Construction des couples (Kuratowski)
+> > Si $x$ et $y$ sont des ensembles, on pose :
+> > $(x, y) = \{ \{ x \}, \{ x, y \} \}$
+^ax-paire
+
+> [!proposition]+ égalité sur les couples
+> Soient $x, y, x', y'$ des ensembles
+> $(x, y) = (x', y') \iff x=x' \wedge y=y'$
+> > [!démonstration]- Démonstration
+> > - $\boxed{\implies}$ Supposons que $x=x'$ et $y=y'$, on a alors $\{ x, y \} = \{ x', y' \}$ et $\{ x \} = \{ x' \}$ par l'axiome d'extension.
+> >   Alors, à nouveau par extentionnalité, on a $\{ \{ x \}, \{ x, y \} \} = \{ \{ x' \}, \{ x', y' \} \}$
+> > - $\boxed{\impliedby}$ Supposons réciproquement que $(x, y) = (x', y')$
+> >   On a alors : $\{ \{ x \}, \{ x, y \} \} = \{ \{ x' \}, \{ x', y' \} \}$
+> >   Il suit par extension que l'un des cas suivants est réalisé :
+> >   - soit $\{ x \} = \{ x' \}$ et $\{ x, y \} = \{ x', y' \}$
+> >     dans ce cas, on a $x=x'$ par extension, et de là il est évident aussi que $y = y'$
+> >   - soit $\{ x \} = \{ x', y' \}$ et $\{ x, y \} = \{ x' \}$
+> >     dans ce cas on sait que l'on doit avoir $x=y$ et $x'=y'$, et on en déduit $\{ x \} = x'$ et $y=y'$
+> >   Les autres cas peuvent être éliminés par extentionnalité.
+
+> [!proposition]+ n-uplets
+> On peut construire les triplets, quadruplets etc. à partir des couples :
+> - $(x, y, z) = ((x, y), z)$
+> - $(x, y, z, w) = (((x, y), z), w)$
+> - $\vdots$ 
+
+> [!proposition]+ Axiome : graphe de la relation $\in$
+> Il existe une classe $E$ telle que pour tous les ensemble $x, y$ on a $(x, y) \in E$ si et seulement si $x \in y$.
+> $\boxed{(x, y) \in E \iff x \in y}$
+> $E$ est le **graphe** de la relation $\in$
+
+> [!proposition]+ Axiome : existence du domaine
+> Si $C$ est une classe, il existe une classe notée $\operatorname{dom}(C)$ telle que pour tout ensemble $x$ on aie $x \in \operatorname{dom}(C)$ si et seulement s'il existe un ensemble $y$ tel que $(x, y) \in C$.
+> $\boxed{x \in \operatorname{dom}(C) \iff \exists y \text{ ensemble},\quad (x, y) \in C}$
+> - i On dit que $\operatorname{dom}(C)$ est le **domaine** de $C$
+^ax-domaine
+
+> [!proposition]+ Axiome : existence du codomaine
+> Si $C$ est une classe, il existe une classe notée $\operatorname{codom}(C)$ telle que pour tout ensemble $y$ on aie $y \in \operatorname{codom}(C)$ si et seulement s'il existe un ensemble $x$ tel que $(x, y) \in C$.
+> $\boxed{y \in \operatorname{codom}(C) \iff \exists x \text{ ensemble},\quad (x, y) \in C}$
+> - i On dit que $\operatorname{codom}(C)$ est le **codomaine** de $C$
+^ax-codomaine
+
+> [!proposition]+ Axiome : existence d'une classe de domaine $C$
+> Si $C$ est une classe, il existe une classe $C'$ dont $C$ est le domaine ($\operatorname{dom}(C') = C$), autrement dit :
+> il existe une classe $C'$ telle que $\forall y \text{ ensemble},\quad (x, y) \in C' \iff x \in C$
+^ax-de-domaine
+
+> [!proposition]+ Axiome : existence d'une classe de codomaine $C$
+> Si $C$ est une classe, il existe une classe $C'$ dont $C$ est le codomaine ($\operatorname{codom}(C') = C$), autrement dit :
+> il existe une classe $C'$ telle que $\forall x \text{ ensemble},\quad (x, y) \in C'$
+^ax-de-codomaine
+
+> [!proposition]+ Axiome : permutation des triplets
+> Soit $C$ une classe, alors :
+> - il existe une classe $D$ telle que pour tous les ensembles $x, y, z$ on aie $(x, y, z) \in D \iff (y, x, z) \in C$
+> - il existe une classe $D'$ telle que pour tout les ensemble $x, y, z$ on aie $(x, y, z) \in D' \iff (x, z, y) \in C$
+> - i ces classes ne sont pas uniquement déterminées par l'axiome d'extension, car leurs "définitions" prescrivent uniquement leurs couples ou trouples.
+
+> [!definition]+ Classe vide
+> Il existe une et une seule classe qui n'a aucun élément.
+> On dit que c'est la classe vide et on la note $\emptyset$
+> > [!démonstration]- Démonstration (existence et unicité)
+> > L'axiome sue le graphe de la relation $\in$ fournit une classe $E$.
+> > On peut alors former la classe $E \cap E^{\complement}$ qui, par construction, n'a aucun élément.
+> > D'après l'axiome d'extentionnalité, c'est la seule telle classe.
+
+> [!proposition]+ Axiome (NBG) : ensemble vide
+> $\emptyset$ est un ensemble
+> - i Sans cet axiome, rien ne garantit l'existence d'ensembles
+
+> [!definition] Univers
+> La classe $U = \emptyset^{\complement}$ est appelée **univers**
+> Par définition on a $x \in U$ pour tout ensemble $x$.
+> Pour toute classe $C$ on a $C \subseteq U$
+> - i Le [[paradoxe de Russell]] montre qu'il existe une classe $R$ qui n'est pas un ensemble. Comme toute sous-classe d'un ensemble est un ensemble aussi, on sait alors que $U$ n'est pas un ensemble.
+^definition
+
+> [!definition] Union d'une classe
+> Soit $C$ une classe
+> Il existe une unique classe dont les éléments sont les éléments des éléments de $C$.
+> On note cette classe $\cup C$ (l'union de $C$).
+> > [!démonstration]- Démonstration (existence et unicité)
+> > L'existence est évidente par définition, mais on peut également utiliser l'union de éléments de $C$.
+> > L'unicité est donnée par l'axiome d'extentionnalité.
+^def-union-monadique
+
+> [!proposition]+ Produit cartésien
+> Soient $A$ et $B$ des classes, il existe une unique classe dont les éléemnts sont les $(x, y)$ avec $x \in A$ et $y \in B$.
+> On note cette classe $A \times B$
+> ---
+> Plus généralement, soit $n \in \mathbb{N}^{*}$, soient $A_1, \dots, A_{n}$ des classes
+> Il existe une classe et une seule dont les éléments sont les $n$-uplets $(x_1, \dots, x_{n})$ avec $x_1 \in A_1, \dots, x_{n} \in A_{n}$
+> On note cette classe $A_1 \times \cdots \times A_{n}$
+> - i Lorsque $A_1 = \cdots = A_{n}$ on note $A_1 \times \cdots \times A_{n} = A^{n}$
+> 
+> > [!démonstration]- Démonstration (existence et unicité)
+> > On sait par l'axiome d'extensionnalité qu'il existe au plus une telle classe (unicité).
+> > Il existe une classe $A'$ telle que $\forall x,\quad (x, y) \in A' \iff y \in A$ (telle que $A = \operatorname{dom}(A')$)
+> > Il existe une classe $B'$ telle que $\forall y,\quad (x, y) \in B' \iff x \in B$ (telle que $B = \operatorname{codom}(B')$)
+> > Alors, $A' \cap B'$ existe (par axiome d'intersection) et convient :
+> > $\forall x,\forall y,\quad (x, y) \in A'\cap B' \implies \begin{cases} x \in A \text{ car } (x, y) \in A' \cap B' \implies (x, y) \in A' \implies x \in A\\ y \in B \text{ car } (x, y) \in B' \end{cases}$
+> > 
+
+> [!proposition]+ Axiome (NBG) : Union d'un ensemble
+> Si $x$ est un ensemble, alors $\cup x$ est un ensemble aussi.
+> $\mathcal{M}(x) \implies \mathcal{M}(\cup x)$
+
+
+## Graphes
+
+> [!definition] Graphe
+> Une classe $C$ est un **graphe** si tous ses éléments sont des couples.
+
+> [!proposition]+ Image directe
+> Soit $G$ un graphe et $C$ une classe.
+> Il existe une unique classe (notée $G[C]$ ou $G\langle C \rangle$) dont les éléments sont les ensembles $y$ tels qu'il existe $x \in C$ vérifiant $(x, y) \in G$
+> Autrement dit :
+> $G[C] = \text{les ensembles } y \text{ tels que } \exists x,\quad x \in C \wedge (x, y) \in G$
+> ou encore : $y \in G[C] \iff \mathcal{M}(y) \wedge (\exists x,\quad x \in C \wedge (x, y) \in G)$
+> > [!démonstration]- Démonstration (existence et unicité)
+> > La classe $G \cap (C \times U)$ a pour éléments les couples $(x, y)$ tels que $x \in C$ et $(x, y) \in G$.
+> > Son [[théorie des ensemble NBC#^ax-codomaine|codomaine]] convient : $G[C] = \operatorname{codom}(G \cap (C \times U))$
+> > Cela montre l'existence de $G[C]$
+> > Son unicité est donnée par extentionnalité
+
+> [!definition] Classe fonctionnelle
+> Une classe $F$ est dite **fonctionnelle** si pour tous ensembles $x, y, z$ tels que $(x, y) \in F$ et $(x, z) \in F$ on a $y = z$
+
+

théorie des modèles . conséquence sémantique.md

@@ -0,0 +1,11 @@
+---
+up:
+tags:
+aliases:
+---
+
+> [!definition] [[théorie des modèles . modèle]]
+> Soit une [[théorie des modèles.théorie|théorie]] $T$ et une [[formule logique close]] $F$ du langage $L$
+> $F$ est **conséquence sémantique** de $T$ (ou simplement conséquence de $T$) si et seulement si toute [[théorie des modèles . 𝐿-structure|𝐿-structure]] qui est modèle de $T$ est aussi modèle de $F$.
+> 
+^definition

théorie des modèles . formule contradictoire.md

@@ -0,0 +1,20 @@
+---
+up:
+  - "[[théorie des modèles . formule universellement valide|formule universellement valide]]"
+tags:
+  - s/maths/logique/modèles
+aliases:
+  - formule contradictoire
+  - contradictoire
+  - formule inconsistante
+  - inconsistante
+---
+
+> [!definition] [[théorie des modèles . formule contradictoire]]
+> Une [[formule logique close|formule close]] d'un [[langage des prédicats du premier ordre|langage]] $L$ est **contradictoire** (ou **inconsistante**) si et seulement sa négation est [[théorie des modèles . formule universellement valide|universellement valide]]
+^definition
+
+# Propriétés
+
+# Exemples
+

théorie des modèles . formule universellement valide.md

@@ -0,0 +1,22 @@
+---
+up:
+  - "[[théorie des modèles]]"
+tags:
+  - s/maths/logique/modèles
+aliases:
+  - formule universellement valide
+  - universellement valide
+---
+
+> [!definition] [[théorie des modèles . formule universellement valide]]
+> Soit $L$ un [[langage des prédicats du premier ordre|langage du premier ordre]]
+> Une [[formule logique close|formule close]] de $L$ est **universellement valide** si et seulement si elle est satisfaite dans toute $L$-structure. (On dit parfois simplement « formule valide »).
+> On note $\vdash^{*}F$ pour « $F$ est universellement valide »
+^definition
+
+
+# Propriétés
+
+# Exemples
+
+

théorie des modèles . modèle.md

@@ -0,0 +1,20 @@
+---
+up:
+  - "[[théorie des modèles]]"
+tags:
+  - "#s/maths/logique/modèles"
+---
+
+
+# Propriétés
+
+# Exemples
+
+
+
+---
+Un modèle logique est  **une [[interprétation]] particulière d'une [[proposition]]**.
+
+On dit qu'une interprétation $I$ est un [[théorie des modèles . modèle]] d'une [[proposition]] logique $\Phi$ ssi $I(\Phi) = \mathbb{V}$.
+
+Si toutes les interprétations de $P$ sont aussi des modèles de $P$, alors on dit que $P$ est une [[tautologie]].

théorie des modèles.md

@@ -0,0 +1,16 @@
+---
+up:
+  - "[[logique]]"
+tags:
+  - s/maths/logique/modèles
+aliases:
+---
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```

troubleshoot.md

@@ -0,0 +1,15 @@
+---
+up:
+tags:
+aliases:
+---
+
+```breadcrumbs
+title: "Sous-notes"
+type: tree
+collapse: true
+show-attributes: [field]
+field-groups: [downs]
+depth: [0, 0]
+```
+

épistémologie . réalisme.md

@@ -8,6 +8,8 @@ aliases:
   - réalisme
 share_link: https://share.note.sx/1ckfabvc#5mTtkYDXoj/rv3sTmsdUqSMHMJStpRbFWBojhX6cpTY
 share_updated: 2025-09-15T13:06:31+02:00
+sibling:
+  - "[[épistémologie . antiréalisme|antiréalisme]]"
 ---
 
 Idée qu'une théorie scientifique est la rencontre de son objet.