diff --git a/package-lock.json b/package-lock.json
index f6516eab..67946a1f 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -19,8 +19,8 @@
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-        "clsx": "^2.0.0",
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+        "fast-glob": "^3.3.2",
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-        "gray-matter": "^4.0.3",
         "hast-util-to-estree": "^3.1.0",
-        "katex": "^0.16.9",
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         "negotiator": "^1.0.0",
-        "p-limit": "^6.0.0",
+        "react-compiler-runtime": "0.0.0-experimental-22c6e49-20241219",
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@@ -5806,11 +5784,12 @@
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         "remark-reading-time": "^2.0.1",
         "remark-smartypants": "^3.0.0",
-        "shiki": "^1.0.0",
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-        "title": "^4.0.0",
+        "title": "^4.0.1",
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+        "unist-util-visit-children": "^3.0.0",
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         "zod": "^3.22.3",
         "zod-validation-error": "^3.0.0"
@@ -5819,36 +5798,100 @@
         "node": ">=18"
       },
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-        "next": ">=13",
+        "next": ">=14",
         "react": ">=18",
         "react-dom": ">=18"
       }
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+      "version": "4.2.13",
+      "resolved": "https://registry.npmjs.org/nextra-theme-docs/-/nextra-theme-docs-4.2.13.tgz",
+      "integrity": "sha512-PO+ltZFtKXe2Jt4hgdJi5JahQHOjt2qmz5wVSfhS+PZDMAuFCa0UubBvkCyQDF3YdKjUI2gJ8CW0fGw84yeseQ==",
       "license": "MIT",
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-        "clsx": "^2.0.0",
-        "escape-string-regexp": "^5.0.0",
-        "flexsearch": "^0.7.43",
+        "clsx": "^2.1.0",
         "next-themes": "^0.4.0",
+        "react-compiler-runtime": "0.0.0-experimental-22c6e49-20241219",
         "scroll-into-view-if-needed": "^3.1.0",
-        "zod": "^3.22.3"
+        "zod": "^3.22.3",
+        "zod-validation-error": "^3.0.0",
+        "zustand": "^5.0.1"
       },
       "peerDependencies": {
-        "next": ">=13",
-        "nextra": "3.3.1",
+        "next": ">=14",
+        "nextra": "4.2.13",
         "react": ">=18",
         "react-dom": ">=18"
       }
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+    "node_modules/nextra/node_modules/@shikijs/core": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/core/-/core-2.5.0.tgz",
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+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/engine-javascript": "2.5.0",
+        "@shikijs/engine-oniguruma": "2.5.0",
+        "@shikijs/types": "2.5.0",
+        "@shikijs/vscode-textmate": "^10.0.2",
+        "@types/hast": "^3.0.4",
+        "hast-util-to-html": "^9.0.4"
+      }
+    },
+    "node_modules/nextra/node_modules/@shikijs/engine-javascript": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/engine-javascript/-/engine-javascript-2.5.0.tgz",
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+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/types": "2.5.0",
+        "@shikijs/vscode-textmate": "^10.0.2",
+        "oniguruma-to-es": "^3.1.0"
+      }
+    },
+    "node_modules/nextra/node_modules/@shikijs/engine-oniguruma": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/engine-oniguruma/-/engine-oniguruma-2.5.0.tgz",
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+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/types": "2.5.0",
+        "@shikijs/vscode-textmate": "^10.0.2"
+      }
+    },
+    "node_modules/nextra/node_modules/@shikijs/langs": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/langs/-/langs-2.5.0.tgz",
+      "integrity": "sha512-Qfrrt5OsNH5R+5tJ/3uYBBZv3SuGmnRPejV9IlIbFH3HTGLDlkqgHymAlzklVmKBjAaVmkPkyikAV/sQ1wSL+w==",
+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/types": "2.5.0"
+      }
+    },
+    "node_modules/nextra/node_modules/@shikijs/themes": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/themes/-/themes-2.5.0.tgz",
+      "integrity": "sha512-wGrk+R8tJnO0VMzmUExHR+QdSaPUl/NKs+a4cQQRWyoc3YFbUzuLEi/KWK1hj+8BfHRKm2jNhhJck1dfstJpiw==",
+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/types": "2.5.0"
+      }
+    },
+    "node_modules/nextra/node_modules/@shikijs/types": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/@shikijs/types/-/types-2.5.0.tgz",
+      "integrity": "sha512-ygl5yhxki9ZLNuNpPitBWvcy9fsSKKaRuO4BAlMyagszQidxcpLAr0qiW/q43DtSIDxO6hEbtYLiFZNXO/hdGw==",
+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/vscode-textmate": "^10.0.2",
+        "@types/hast": "^3.0.4"
+      }
+    },
     "node_modules/nextra/node_modules/@theguild/remark-mermaid": {
-      "version": "0.1.3",
-      "resolved": "https://registry.npmjs.org/@theguild/remark-mermaid/-/remark-mermaid-0.1.3.tgz",
-      "integrity": "sha512-2FjVlaaKXK7Zj7UJAgOVTyaahn/3/EAfqYhyXg0BfDBVUl+lXcoIWRaxzqfnDr2rv8ax6GsC5mNh6hAaT86PDw==",
+      "version": "0.2.0",
+      "resolved": "https://registry.npmjs.org/@theguild/remark-mermaid/-/remark-mermaid-0.2.0.tgz",
+      "integrity": "sha512-o8n57TJy0OI4PCrNw8z6S+vpHtrwoQZzTA5Y3fL0U1NDRIoMg/78duWgEBFsCZcWM1G6zjE91yg1aKCsDwgE2Q==",
       "license": "MIT",
       "dependencies": {
         "mermaid": "^11.0.0",
@@ -5858,6 +5901,51 @@
         "react": "^18.2.0"
       }
     },
+    "node_modules/nextra/node_modules/oniguruma-to-es": {
+      "version": "3.1.0",
+      "resolved": "https://registry.npmjs.org/oniguruma-to-es/-/oniguruma-to-es-3.1.0.tgz",
+      "integrity": "sha512-BJ3Jy22YlgejHSO7Fvmz1kKazlaPmRSUH+4adTDUS/dKQ4wLxI+gALZ8updbaux7/m7fIlpgOZ5fp/Inq5jUAw==",
+      "license": "MIT",
+      "dependencies": {
+        "emoji-regex-xs": "^1.0.0",
+        "regex": "^6.0.1",
+        "regex-recursion": "^6.0.2"
+      }
+    },
+    "node_modules/nextra/node_modules/regex": {
+      "version": "6.0.1",
+      "resolved": "https://registry.npmjs.org/regex/-/regex-6.0.1.tgz",
+      "integrity": "sha512-uorlqlzAKjKQZ5P+kTJr3eeJGSVroLKoHmquUj4zHWuR+hEyNqlXsSKlYYF5F4NI6nl7tWCs0apKJ0lmfsXAPA==",
+      "license": "MIT",
+      "dependencies": {
+        "regex-utilities": "^2.3.0"
+      }
+    },
+    "node_modules/nextra/node_modules/regex-recursion": {
+      "version": "6.0.2",
+      "resolved": "https://registry.npmjs.org/regex-recursion/-/regex-recursion-6.0.2.tgz",
+      "integrity": "sha512-0YCaSCq2VRIebiaUviZNs0cBz1kg5kVS2UKUfNIx8YVs1cN3AV7NTctO5FOKBA+UT2BPJIWZauYHPqJODG50cg==",
+      "license": "MIT",
+      "dependencies": {
+        "regex-utilities": "^2.3.0"
+      }
+    },
+    "node_modules/nextra/node_modules/shiki": {
+      "version": "2.5.0",
+      "resolved": "https://registry.npmjs.org/shiki/-/shiki-2.5.0.tgz",
+      "integrity": "sha512-mI//trrsaiCIPsja5CNfsyNOqgAZUb6VpJA+340toL42UpzQlXpwRV9nch69X6gaUxrr9kaOOa6e3y3uAkGFxQ==",
+      "license": "MIT",
+      "dependencies": {
+        "@shikijs/core": "2.5.0",
+        "@shikijs/engine-javascript": "2.5.0",
+        "@shikijs/engine-oniguruma": "2.5.0",
+        "@shikijs/langs": "2.5.0",
+        "@shikijs/themes": "2.5.0",
+        "@shikijs/types": "2.5.0",
+        "@shikijs/vscode-textmate": "^10.0.2",
+        "@types/hast": "^3.0.4"
+      }
+    },
     "node_modules/nlcst-to-string": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/nlcst-to-string/-/nlcst-to-string-4.0.0.tgz",
@@ -5956,27 +6044,13 @@
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       "integrity": "sha512-bwALDxriqfKGfUufKGGepCzu9x7nJQuoRoAFp4AnwehhC2crqrDIAP/uN2qdlsAvSMpeRC3+Yzhqc7hLmle5+g==",
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "emoji-regex-xs": "^1.0.0",
         "regex": "^5.1.1",
         "regex-recursion": "^5.1.1"
       }
     },
-    "node_modules/p-limit": {
-      "version": "6.2.0",
-      "resolved": "https://registry.npmjs.org/p-limit/-/p-limit-6.2.0.tgz",
-      "integrity": "sha512-kuUqqHNUqoIWp/c467RI4X6mmyuojY5jGutNU0wVTmEOOfcuwLqyMVoAi9MKi2Ak+5i9+nhmrK4ufZE8069kHA==",
-      "license": "MIT",
-      "dependencies": {
-        "yocto-queue": "^1.1.1"
-      },
-      "engines": {
-        "node": ">=18"
-      },
-      "funding": {
-        "url": "https://github.com/sponsors/sindresorhus"
-      }
-    },
     "node_modules/package-manager-detector": {
       "version": "0.2.9",
       "resolved": "https://registry.npmjs.org/package-manager-detector/-/package-manager-detector-0.2.9.tgz",
@@ -6196,6 +6270,15 @@
         "node": ">=0.10.0"
       }
     },
+    "node_modules/react-compiler-runtime": {
+      "version": "0.0.0-experimental-22c6e49-20241219",
+      "resolved": "https://registry.npmjs.org/react-compiler-runtime/-/react-compiler-runtime-0.0.0-experimental-22c6e49-20241219.tgz",
+      "integrity": "sha512-bOAGaRL1ldfIIpbDsl+uV025Ta6RS6/cOjvvh8r2Vo7KtqB+RSvihVYRsWQz7ECKNPWdq5MClS845acwAwieDw==",
+      "license": "MIT",
+      "peerDependencies": {
+        "react": "^17.0.0 || ^18.0.0 || ^19.0.0"
+      }
+    },
     "node_modules/react-dom": {
       "version": "19.0.0",
       "resolved": "https://registry.npmjs.org/react-dom/-/react-dom-19.0.0.tgz",
@@ -6305,6 +6388,7 @@
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       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "regex-utilities": "^2.3.0"
       }
@@ -6314,6 +6398,7 @@
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       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "regex": "^5.1.1",
         "regex-utilities": "^2.3.0"
@@ -6769,19 +6854,6 @@
         "compute-scroll-into-view": "^3.0.2"
       }
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-    "node_modules/section-matter": {
-      "version": "1.0.0",
-      "resolved": "https://registry.npmjs.org/section-matter/-/section-matter-1.0.0.tgz",
-      "integrity": "sha512-vfD3pmTzGpufjScBh50YHKzEu2lxBWhVEHsNGoEXmCmn2hKGfeNLYMzCJpe8cD7gqX7TJluOVpBkAequ6dgMmA==",
-      "license": "MIT",
-      "dependencies": {
-        "extend-shallow": "^2.0.1",
-        "kind-of": "^6.0.0"
-      },
-      "engines": {
-        "node": ">=4"
-      }
-    },
     "node_modules/semver": {
       "version": "7.7.1",
       "resolved": "https://registry.npmjs.org/semver/-/semver-7.7.1.tgz",
@@ -6859,6 +6931,7 @@
       "resolved": "https://registry.npmjs.org/shiki/-/shiki-1.29.2.tgz",
       "integrity": "sha512-njXuliz/cP+67jU2hukkxCNuH1yUi4QfdZZY+sMr5PPrIyXSu5iTb/qYC4BiWWB0vZ+7TbdvYUCeL23zpwCfbg==",
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "@shikijs/core": "1.29.2",
         "@shikijs/engine-javascript": "1.29.2",
@@ -6954,12 +7027,6 @@
         "node": "^12.20.0 || >=14"
       }
     },
-    "node_modules/sprintf-js": {
-      "version": "1.0.3",
-      "resolved": "https://registry.npmjs.org/sprintf-js/-/sprintf-js-1.0.3.tgz",
-      "integrity": "sha512-D9cPgkvLlV3t3IzL0D0YLvGA9Ahk4PcvVwUbN0dSGr1aP0Nrt4AEnTUbuGvquEC0mA64Gqt1fzirlRs5ibXx8g==",
-      "license": "BSD-3-Clause"
-    },
     "node_modules/streamsearch": {
       "version": "1.1.0",
       "resolved": "https://registry.npmjs.org/streamsearch/-/streamsearch-1.1.0.tgz",
@@ -6982,15 +7049,6 @@
         "url": "https://github.com/sponsors/wooorm"
       }
     },
-    "node_modules/strip-bom-string": {
-      "version": "1.0.0",
-      "resolved": "https://registry.npmjs.org/strip-bom-string/-/strip-bom-string-1.0.0.tgz",
-      "integrity": "sha512-uCC2VHvQRYu+lMh4My/sFNmF2klFymLX1wHJeXnbEJERpV/ZsVuonzerjfrGpIGF7LBVa1O7i9kjiWvJiFck8g==",
-      "license": "MIT",
-      "engines": {
-        "node": ">=0.10.0"
-      }
-    },
     "node_modules/strip-final-newline": {
       "version": "3.0.0",
       "resolved": "https://registry.npmjs.org/strip-final-newline/-/strip-final-newline-3.0.0.tgz",
@@ -7545,18 +7603,6 @@
         "node": ">= 14"
       }
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-    "node_modules/yocto-queue": {
-      "version": "1.1.1",
-      "resolved": "https://registry.npmjs.org/yocto-queue/-/yocto-queue-1.1.1.tgz",
-      "integrity": "sha512-b4JR1PFR10y1mKjhHY9LaGo6tmrgjit7hxVIeAmyMw3jegXR4dhYqLaQF5zMXZxY7tLpMyJeLjr1C4rLmkVe8g==",
-      "license": "MIT",
-      "engines": {
-        "node": ">=12.20"
-      },
-      "funding": {
-        "url": "https://github.com/sponsors/sindresorhus"
-      }
-    },
     "node_modules/zod": {
       "version": "3.24.1",
       "resolved": "https://registry.npmjs.org/zod/-/zod-3.24.1.tgz",
@@ -7578,6 +7624,35 @@
         "zod": "^3.18.0"
       }
     },
+    "node_modules/zustand": {
+      "version": "5.0.3",
+      "resolved": "https://registry.npmjs.org/zustand/-/zustand-5.0.3.tgz",
+      "integrity": "sha512-14fwWQtU3pH4dE0dOpdMiWjddcH+QzKIgk1cl8epwSE7yag43k/AD/m4L6+K7DytAOr9gGBe3/EXj9g7cdostg==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=12.20.0"
+      },
+      "peerDependencies": {
+        "@types/react": ">=18.0.0",
+        "immer": ">=9.0.6",
+        "react": ">=18.0.0",
+        "use-sync-external-store": ">=1.2.0"
+      },
+      "peerDependenciesMeta": {
+        "@types/react": {
+          "optional": true
+        },
+        "immer": {
+          "optional": true
+        },
+        "react": {
+          "optional": true
+        },
+        "use-sync-external-store": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/zwitch": {
       "version": "2.0.4",
       "resolved": "https://registry.npmjs.org/zwitch/-/zwitch-2.0.4.tgz",
diff --git a/package.json b/package.json
index 79bcc4da..a250f16d 100644
--- a/package.json
+++ b/package.json
@@ -22,8 +22,8 @@
     "framer-motion": "^12.0.0",
     "next": "^15.0.0",
     "next-sitemap": "^4.2.3",
-    "nextra": "^3.0.0",
-    "nextra-theme-docs": "^3.0.0",
+    "nextra": "^4.0.0",
+    "nextra-theme-docs": "^4.0.0",
     "react": "^19.0.0",
     "react-dom": "^19.0.0",
     "sharp": "^0.33.5"