feat: optimize SEO based on GSC data

- Fix broken hreflang: /en/ ghost page removed, all hreflang point to canonical /
- Add canonical URL tag
- Remove emoji from page titles
- Rewrite title/description with target keywords (LaTeX OCR, math formula recognition, handwriting math)
- Add JSON-LD WebApplication structured data schema
- Update og:image to clean URL without OSS params, add og:image dimensions
- Fix favicon reference from vite.svg to favicon.png
- Add public/sitemap.xml with hreflang annotations
- Add public/robots.txt pointing to sitemap
- Update seoHelper.ts keywords for both zh/en to match search intent
- Add CLAUDE.md project documentation

CLAUDE.md

@@ -0,0 +1,76 @@
+# CLAUDE.md
+
+This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
+
+## Commands
+
+```bash
+# Development server
+npm run dev
+
+# Build
+npm run build          # production
+npm run build:dev      # development build (VITE_ENV=development)
+npm run build:prod     # production build (VITE_ENV=production)
+
+# Type checking
+npm run typecheck
+
+# Linting
+npm run lint
+
+# Unit tests (vitest)
+npm run test           # run once
+npm run test:watch     # watch mode
+
+# E2E tests (playwright)
+npm run test:e2e
+```
+
+To run a single unit test file:
+```bash
+npx vitest run src/components/__tests__/AuthModal.test.tsx
+```
+
+## Architecture
+
+### Provider Tree
+`main.tsx` wraps everything in: `BrowserRouter → AuthProvider → LanguageProvider → AppRouter`
+
+### Routing
+Only two routes (`src/routes/AppRouter.tsx`):
+- `/` → `App` (main app)
+- `/auth/google/callback` → `AuthCallbackPage` (Google OAuth callback handler)
+
+### Auth System
+- **`AuthContext.tsx`** — React context providing `signIn`, `signUp`, `beginGoogleOAuth`, `completeGoogleOAuth`, `signOut`. Uses `useReducer` with `authMachine.ts`.
+- **`authMachine.ts`** — Pure reducer + state types (`AuthPhase`, `AuthState`, `AuthAction`). No side effects — all async logic lives in `AuthContext`.
+- **`authService.ts`** — Calls backend API for login/register/Google OAuth/user info. Decodes JWT payload client-side to extract `UserInfo`. Handles session restore from `localStorage`.
+- **`lib/api.ts`** — `http` client wrapper with `tokenManager` (stores JWT in `localStorage` under key `texpixel_token`). Adds `Authorization` header automatically. Throws `ApiError` for non-success business codes.
+
+### Environment / API
+- **`src/config/env.ts`** — Switches API base URL based on `VITE_ENV` env var:
+  - `development`: `https://cloud.texpixel.com:10443/doc_ai/v1`
+  - `production`: `https://api.texpixel.com/doc_ai/v1`
+- The API uses a custom response envelope: `{ request_id, code, message, data }`. Success is `code === 200` (some endpoints also accept `0`).
+
+### Main App Flow (`App.tsx`)
+Three-panel layout: `LeftSidebar | FilePreview | ResultPanel`
+
+Core data flow:
+1. On auth, `loadFiles()` fetches paginated task history from `/task/list`
+2. File upload goes: compute MD5 → get OSS pre-signed URL (`/oss/signature_url`) → PUT to OSS → create task (`/formula/recognition`) → poll every 2s for result
+3. Results cached in `resultsCache` ref (keyed by `task_id`) to avoid redundant API calls
+4. Guest users get 3 free uploads tracked via `localStorage` (`texpixel_guest_usage_count`)
+
+### Internationalization
+`LanguageContext.tsx` supports `en` / `zh`. Language is auto-detected via IP (`lib/ipLocation.ts`) on first visit, persisted to `localStorage` on manual switch. All UI strings come from `lib/translations.ts` via `const { t } = useLanguage()`.
+
+### Key Type Definitions
+- `src/types/api.ts` — All API request/response types, `TaskStatus` enum, `ApiErrorCode` enum, `ApiErrorMessages` map
+- `src/types/index.ts` — Internal app types (`FileRecord`, `RecognitionResult`)
+
+### Tests
+- Unit tests: `src/components/__tests__/` and `src/contexts/__tests__/`, run with vitest + jsdom + `@testing-library/react`
+- E2E tests: `e2e/` directory, run with Playwright
+- Setup file: `src/test/setup.ts`