diff --git a/docs-site/package-lock.json b/docs-site/package-lock.json
index 41612e6..8a75067 100644
--- a/docs-site/package-lock.json
+++ b/docs-site/package-lock.json
@@ -8,7 +8,7 @@
       "name": "ppe-docs",
       "version": "0.0.1",
       "dependencies": {
-        "@astrojs/starlight": "^0.41",
+        "@astrojs/starlight": "^0.42",
         "astro": "^7.2",
         "rehype-katex": "^7.0.1",
         "remark-math": "^6.0.0",
@@ -16,29 +16,46 @@
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-      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding/-/compiler-binding-0.3.2.tgz",
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding/-/compiler-binding-0.4.1.tgz",
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       "license": "MIT",
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         "node": "^20.19.0 || >=22.12.0"
       },
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-        "@astrojs/compiler-binding-linux-x64-gnu": "0.3.2",
-        "@astrojs/compiler-binding-linux-x64-musl": "0.3.2",
-        "@astrojs/compiler-binding-wasm32-wasi": "0.3.2",
-        "@astrojs/compiler-binding-win32-arm64-msvc": "0.3.2",
-        "@astrojs/compiler-binding-win32-x64-msvc": "0.3.2"
+        "@astrojs/compiler-binding-android-arm64": "0.4.1",
+        "@astrojs/compiler-binding-darwin-arm64": "0.4.1",
+        "@astrojs/compiler-binding-darwin-x64": "0.4.1",
+        "@astrojs/compiler-binding-linux-arm64-gnu": "0.4.1",
+        "@astrojs/compiler-binding-linux-arm64-musl": "0.4.1",
+        "@astrojs/compiler-binding-linux-x64-gnu": "0.4.1",
+        "@astrojs/compiler-binding-linux-x64-musl": "0.4.1",
+        "@astrojs/compiler-binding-wasm32-wasi": "0.4.1",
+        "@astrojs/compiler-binding-win32-arm64-msvc": "0.4.1",
+        "@astrojs/compiler-binding-win32-x64-msvc": "0.4.1"
+      }
+    },
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+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-android-arm64/-/compiler-binding-android-arm64-0.4.1.tgz",
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+      "cpu": [
+        "arm64"
+      ],
+      "license": "MIT",
+      "optional": true,
+      "os": [
+        "android"
+      ],
+      "engines": {
+        "node": "^20.19.0 || >=22.12.0"
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-      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-darwin-arm64/-/compiler-binding-darwin-arm64-0.3.2.tgz",
-      "integrity": "sha512-MM8tn8CSimcfytaOla4b6acN8mKWiL/rlAA1fpT3/Wl7dNGSE4y8FjTN/zJVNnb63CsLWG5zZwCt01TXtDKh9g==",
+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-darwin-arm64/-/compiler-binding-darwin-arm64-0.4.1.tgz",
+      "integrity": "sha512-7iwXcU+hB60Y1SvOfnWHNioT72gDsDQKaDipXh2Onwp/TvQMozhbvhy13wJR8Af940a0h6PbddCeJFpj791UDA==",
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@@ -52,9 +69,9 @@
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-darwin-x64/-/compiler-binding-darwin-x64-0.4.1.tgz",
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@@ -68,12 +85,15 @@
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-linux-arm64-gnu/-/compiler-binding-linux-arm64-gnu-0.4.1.tgz",
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       "cpu": [
         "arm64"
       ],
+      "libc": [
+        "glibc"
+      ],
       "license": "MIT",
       "optional": true,
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@@ -84,12 +104,15 @@
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+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-linux-arm64-musl/-/compiler-binding-linux-arm64-musl-0.4.1.tgz",
+      "integrity": "sha512-a3EW27f+Z9uf57vYmpLgUriA1y9wDhKz57PT8D8XlFZt2HZEWhUxKuxI1jvKVI9p8okYee11WXEm/FHY1G9yoQ==",
       "cpu": [
         "arm64"
       ],
+      "libc": [
+        "musl"
+      ],
       "license": "MIT",
       "optional": true,
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@@ -100,12 +123,15 @@
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-linux-x64-gnu/-/compiler-binding-linux-x64-gnu-0.4.1.tgz",
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       "cpu": [
         "x64"
       ],
+      "libc": [
+        "glibc"
+      ],
       "license": "MIT",
       "optional": true,
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@@ -116,12 +142,15 @@
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+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-linux-x64-musl/-/compiler-binding-linux-x64-musl-0.4.1.tgz",
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       "cpu": [
         "x64"
       ],
+      "libc": [
+        "musl"
+      ],
       "license": "MIT",
       "optional": true,
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@@ -132,25 +161,25 @@
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-      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-wasm32-wasi/-/compiler-binding-wasm32-wasi-0.3.2.tgz",
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+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-wasm32-wasi/-/compiler-binding-wasm32-wasi-0.4.1.tgz",
+      "integrity": "sha512-vNLxIv41ZE+nmPFtw24cRW5ZXG+ZPcAGtgigtjCP8lvcxKI7u2GrXoMsCgEH5fMw8WCEJpwLvsVBg15rJKAkyA==",
       "cpu": [
         "wasm32"
       ],
       "license": "MIT",
       "optional": true,
       "dependencies": {
-        "@napi-rs/wasm-runtime": "^1.2.0"
+        "@napi-rs/wasm-runtime": "^1.2.4"
       },
       "engines": {
         "node": ">=14.0.0"
       }
     },
     "node_modules/@astrojs/compiler-binding-win32-arm64-msvc": {
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-      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-win32-arm64-msvc/-/compiler-binding-win32-arm64-msvc-0.3.2.tgz",
-      "integrity": "sha512-ESruf+6Qkl1trHUFxI6GSf6t52j8yN2kCNSzMWdzt7V/T09tFHrYzrVaJQohb2C9bJUH76pNvX6Zb51+xCQc9Q==",
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-win32-arm64-msvc/-/compiler-binding-win32-arm64-msvc-0.4.1.tgz",
+      "integrity": "sha512-/xTDgRsFDoTh0/+KFXJ74DY4Jqn8CoSHwa8UP5RAblHfnRHkenwfSl4zYDET61O9vXKLk09UzHjjq09yP20/AQ==",
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@@ -164,9 +193,9 @@
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-      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-win32-x64-msvc/-/compiler-binding-win32-x64-msvc-0.3.2.tgz",
-      "integrity": "sha512-wzzVrEbOwbsLWOdEbocskjMRx2aZPxJ7ZbmL+jnpBamFwmigm+2M/wzuM6JWncocgYwLic1csSpalBh96kQKXA==",
+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-binding-win32-x64-msvc/-/compiler-binding-win32-x64-msvc-0.4.1.tgz",
+      "integrity": "sha512-0x5J6iHZO0Fjo/CVzoIbXKzWnGESftDbEUQ/oXQ61HhUAFoR7+T1jfToZSNAS+gYyBXHSTpMWYC7lzarbhClcg==",
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@@ -180,21 +209,21 @@
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+      "resolved": "https://registry.npmjs.org/@astrojs/compiler-rs/-/compiler-rs-0.4.1.tgz",
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       "license": "MIT",
       "dependencies": {
-        "@astrojs/compiler-binding": "0.3.2"
+        "@astrojs/compiler-binding": "0.4.1"
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       }
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     "node_modules/@astrojs/internal-helpers": {
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-      "resolved": "https://registry.npmjs.org/@astrojs/internal-helpers/-/internal-helpers-0.10.2.tgz",
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+      "resolved": "https://registry.npmjs.org/@astrojs/internal-helpers/-/internal-helpers-0.11.0.tgz",
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@@ -207,74 +236,38 @@
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+      "integrity": "sha512-g4QehXnB/MzxQWnSf17NciFInMqEJy9948p8cc7zGg/r7995m0Ln5PMr3Xlnj24iey1LchaoZ3SzTOa3D4P/3w==",
       "license": "MIT",
       "dependencies": {
-        "@astrojs/internal-helpers": "0.10.2",
+        "@astrojs/internal-helpers": "0.11.0",
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         "github-slugger": "^2.0.0",
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-        "satteri": "^0.9.1"
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     "node_modules/@astrojs/mdx": {
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-      "resolved": "https://registry.npmjs.org/@astrojs/mdx/-/mdx-7.0.5.tgz",
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+        "@astrojs/internal-helpers": "0.11.0",
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       "peerDependencies": {
-        "@astrojs/markdown-satteri": "^0.3.1",
-        "astro": "^7.0.0"
+        "@astrojs/markdown-remark": "^7.3.0",
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-        "@astrojs/markdown-satteri": {
+        "@astrojs/markdown-remark": {
           "optional": true
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@@ -303,44 +296,43 @@
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-      "resolved": "https://registry.npmjs.org/@astrojs/starlight/-/starlight-0.41.7.tgz",
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+      "version": "0.42.3",
+      "resolved": "https://registry.npmjs.org/@astrojs/starlight/-/starlight-0.42.3.tgz",
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       "license": "MIT",
       "dependencies": {
-        "@astrojs/markdown-satteri": "^0.3.5",
-        "@astrojs/mdx": "^7.0.5",
+        "@astrojs/markdown-satteri": "^0.4.0",
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         "klona": "^2.0.6",
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-        "satteri": "^0.9.1",
+        "satteri": "^0.10.3",
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         "vfile": "^6.0.3"
       },
       "peerDependencies": {
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-        "astro": "^7.0.2"
+        "@astrojs/markdown-remark": "^7.3.0",
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       "peerDependenciesMeta": {
         "@astrojs/markdown-remark": {
@@ -410,9 +402,9 @@
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-      "integrity": "sha512-RgmdTfSBOg04sdPcpTSD1jzoNBjt9a80/ZCzp5cI9n1qPzLZWF9YdvWGN2zmTumP1HWhXKdUWexjy/Wy/lJ7tA==",
-      "license": "MIT",
-      "dependencies": {
-        "@types/unist": "^3.0.0"
-      },
-      "funding": {
-        "type": "opencollective",
-        "url": "https://opencollective.com/unified"
-      }
-    },
     "node_modules/unist-util-visit-parents": {
       "version": "6.0.2",
       "resolved": "https://registry.npmjs.org/unist-util-visit-parents/-/unist-util-visit-parents-6.0.2.tgz",
@@ -6846,6 +5554,18 @@
       "integrity": "sha512-EPD5q1uXyFxJpCrLnCc1nHnq3gOa6DZBocAIiI2TaSCA7VCJ1UJDMagCzIkXNsUYfD1daK//LTEQ8xiIbrHtcw==",
       "license": "MIT"
     },
+    "node_modules/verkit": {
+      "version": "0.4.1",
+      "resolved": "https://registry.npmjs.org/verkit/-/verkit-0.4.1.tgz",
+      "integrity": "sha512-mMVzj0TXExtVdlDEq+Mzp0eyOuyznNpFobNM3uAqe3HVm/Ps2c+u17BligMkZjZCA6EiXpoon8iRTer3iu40SQ==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=18.12.0"
+      },
+      "funding": {
+        "url": "https://github.com/sponsors/sxzz"
+      }
+    },
     "node_modules/vfile": {
       "version": "6.0.3",
       "resolved": "https://registry.npmjs.org/vfile/-/vfile-6.0.3.tgz",
@@ -7022,9 +5742,9 @@
       }
     },
     "node_modules/zod": {
-      "version": "4.4.3",
-      "resolved": "https://registry.npmjs.org/zod/-/zod-4.4.3.tgz",
-      "integrity": "sha512-ytENFjIJFl2UwYglde2jchW2Hwm4GJFLDiSXWdTrJQBIN9Fcyp7n4DhxJEiWNAJMV1/BqWfW/kkg71UDcHJyTQ==",
+      "version": "4.6.5",
+      "resolved": "https://registry.npmjs.org/zod/-/zod-4.6.5.tgz",
+      "integrity": "sha512-v5l/aFXZQeai4awLbOpSoHecE9UiMrnfx75tEXLjNonXVARxQ5mOeipTjROUchszUNCqnE+hqAMujRsRHsut2Q==",
       "license": "MIT",
       "funding": {
         "url": "https://github.com/sponsors/colinhacks"
diff --git a/docs-site/package.json b/docs-site/package.json
index 8148d84..4f47237 100644
--- a/docs-site/package.json
+++ b/docs-site/package.json
@@ -14,7 +14,7 @@
     "astro": "astro"
   },
   "dependencies": {
-    "@astrojs/starlight": "^0.41",
+    "@astrojs/starlight": "^0.42",
     "astro": "^7.2",
     "rehype-katex": "^7.0.1",
     "remark-math": "^6.0.0",