chore: add katex, dompurify, vitest; copy sample exam files

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/package.json

@@ -0,0 +1,41 @@
+{
+  "name": "frontend",
+  "private": true,
+  "version": "0.0.0",
+  "type": "module",
+  "scripts": {
+    "dev": "vite",
+    "build": "tsc -b && vite build",
+    "lint": "eslint .",
+    "preview": "vite preview",
+    "test": "vitest",
+    "test:run": "vitest run"
+  },
+  "dependencies": {
+    "dompurify": "^3.4.1",
+    "katex": "^0.16.45",
+    "react": "^19.2.5",
+    "react-dom": "^19.2.5"
+  },
+  "devDependencies": {
+    "@babel/core": "^7.29.0",
+    "@eslint/js": "^9.39.4",
+    "@rolldown/plugin-babel": "^0.2.3",
+    "@types/babel__core": "^7.20.5",
+    "@types/dompurify": "^3.0.5",
+    "@types/node": "^24.12.2",
+    "@types/react": "^19.2.14",
+    "@types/react-dom": "^19.2.3",
+    "@vitejs/plugin-react": "^6.0.1",
+    "@vitest/coverage-v8": "^4.1.5",
+    "babel-plugin-react-compiler": "^1.0.0",
+    "eslint": "^9.39.4",
+    "eslint-plugin-react-hooks": "^7.1.1",
+    "eslint-plugin-react-refresh": "^0.5.2",
+    "globals": "^17.5.0",
+    "typescript": "~6.0.2",
+    "typescript-eslint": "^8.58.2",
+    "vite": "^8.0.9",
+    "vitest": "^4.1.5"
+  }
+}