feat: optimize docs pages and add 4 new doc articles (en + zh)

- Rewrote DocsListPage and DocDetailPage with landing.css aesthetic
  (icon cards, skeleton loader, prose styles, CTA box)
- Added docs-specific CSS to landing.css
- Created image-to-latex, copy-to-word, ocr-accuracy, pdf-extraction
  articles in both English and Chinese
- Updated DocsSeoSection guide cards to link to real doc slugs

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

content/docs/en/copy-to-word.md

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+---
+title: Copy to Word
+description: Export recognized formulas directly into Microsoft Word as editable equations
+slug: copy-to-word
+date: 2026-03-25
+tags: [export, Word, DOCX]
+order: 4
+---
+
+# Copy to Word
+
+TexPixel can export your recognized formulas directly into Microsoft Word as native, editable equations — not images. This means you can continue editing the formula inside Word after export.
+
+## How to Export to Word
+
+1. Upload your formula image and wait for recognition to complete.
+2. Click the **Export** button in the result panel.
+3. Select **DOCX** from the file export options.
+4. Download the file and open it in Microsoft Word.
+
+The downloaded `.docx` file contains your formula as a native Word equation (OMML format), which Word renders using its built-in equation editor.
+
+## Why Use DOCX Export?
+
+| Method | Editable in Word | Renders Correctly | Copy-Paste |
+|---|---|---|---|
+| Screenshot / image | No | Yes | No |
+| LaTeX string | No (without plugin) | No | Yes |
+| DOCX export | **Yes** | **Yes** | N/A |
+
+The DOCX format is ideal when you need to:
+- Submit homework or reports as Word documents
+- Share formulas with colleagues who don't use LaTeX
+- Continue editing the formula after export
+
+## Inserting into an Existing Document
+
+If you want to insert a formula into an existing Word document rather than starting fresh:
+
+1. Open the downloaded `.docx` file in Word.
+2. Select the equation and copy it (`Ctrl+C` / `Cmd+C`).
+3. Paste it into your target document (`Ctrl+V` / `Cmd+V`).
+
+Word preserves the equation formatting during paste.
+
+## Mixed Content (Text + Formulas)
+
+If your upload contains a mix of regular text and formulas (e.g., a textbook page), use DOCX export — it's the only format that handles mixed content correctly. LaTeX and MathML export are only available for pure-formula results.
+
+> **Note:** For mixed-content results, LaTeX/MathML export is disabled. Use DOCX to get a properly formatted document with both text and equations.
+
+## Compatibility
+
+DOCX export is compatible with:
+- Microsoft Word 2016 and later (Windows and Mac)
+- Google Docs (equations render as images when imported)
+- LibreOffice Writer (partial support)
+
+## Tips
+
+- After pasting into Word, double-click the equation to open the equation editor and make changes.
+- If the formula looks different from expected, try re-uploading a higher-resolution image for a more accurate recognition result.
+
+---
+
+[Try exporting a formula to Word →](/app)

content/docs/en/image-to-latex.md

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+---
+title: Image to LaTeX
+description: How to convert any formula image into clean LaTeX code with TexPixel
+slug: image-to-latex
+date: 2026-03-25
+tags: [LaTeX, tutorial]
+order: 2
+---
+
+# Image to LaTeX
+
+TexPixel's core feature is converting formula images — from photos, scans, or screenshots — directly into LaTeX code you can paste anywhere.
+
+## How It Works
+
+1. **Upload your image** — Drag and drop a JPG or PNG into the upload zone, or click to browse. You can also paste from your clipboard.
+2. **AI processes it** — Our model detects the formula region, runs OCR, and generates structured LaTeX in under a second.
+3. **Copy the result** — Click the copy button next to the LaTeX output. Paste directly into Overleaf, VS Code, Word, or any LaTeX editor.
+
+## Input Requirements
+
+| Requirement | Details |
+|---|---|
+| File formats | JPG, PNG |
+| Max file size | 10 MB |
+| Recommended DPI | 150 DPI or higher |
+| Background | White or light backgrounds work best |
+
+## What Gets Recognized
+
+TexPixel handles a wide range of mathematical content:
+
+- **Algebra** — equations, inequalities, polynomials
+- **Calculus** — derivatives, integrals, limits
+- **Matrices** — 2×2 up to large arrays
+- **Greek letters** — α, β, γ, Σ, Π, and more
+- **Subscripts and superscripts** — `x_i^2`, `a_{n+1}`
+- **Fractions** — `\frac{a}{b}`, nested fractions
+- **Square roots and radicals** — `\sqrt{x}`, `\sqrt[n]{x}`
+
+## Example
+
+Uploading an image of the quadratic formula gives you:
+
+```latex
+x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+```
+
+An image of an integral:
+
+```latex
+\int_0^\infty e^{-x^2}\, dx = \frac{\sqrt{\pi}}{2}
+```
+
+## Tips for Best Results
+
+- **Use clear images** — avoid blur, shadows, or low contrast
+- **Crop tightly** — the less background, the better the focus
+- **Dark ink on white paper** — ideal for handwritten formulas
+- **Avoid rotated images** — keep the formula horizontal
+- **One formula per image** — for complex multi-part work, crop each formula separately
+
+## Limitations
+
+- Extremely faint or pencil-written formulas may have lower accuracy
+- Hand-drawn arrows or annotation marks outside the formula may be ignored
+- Very large matrices (10×10+) may have reduced accuracy
+
+## Copy Options
+
+After recognition, you can copy output in multiple formats:
+
+- **LaTeX** — raw LaTeX string
+- **MathML** — for web embedding
+- **Markdown** — `$...$` inline or `$$...$$` block
+- **Plain text** — Unicode approximation
+
+---
+
+Ready to try it? [Upload a formula image now →](/app)

content/docs/en/ocr-accuracy.md

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+---
+title: OCR Accuracy
+description: Understanding TexPixel recognition accuracy and how to get the best results
+slug: ocr-accuracy
+date: 2026-03-25
+tags: [accuracy, tips]
+order: 5
+---
+
+# OCR Accuracy
+
+TexPixel achieves industry-leading accuracy on mathematical formula recognition — but accuracy isn't uniform across all input types. This guide explains what affects accuracy and how to maximize it.
+
+## Accuracy by Formula Type
+
+| Formula Type | Typical Accuracy |
+|---|---|
+| Printed formulas (textbooks, papers) | 95–99% |
+| Clean handwritten formulas | 88–95% |
+| Scanned documents (300 DPI+) | 93–98% |
+| Photos of whiteboards | 82–92% |
+| Low-resolution images (< 72 DPI) | 60–80% |
+
+These are approximate ranges. Individual results depend heavily on image quality.
+
+## Factors That Affect Accuracy
+
+### Image Quality
+
+The single biggest factor. A blurry, low-resolution, or poorly lit image will always produce worse results than a clean scan.
+
+- **Resolution** — 150 DPI or higher is recommended. 300 DPI is ideal for documents.
+- **Contrast** — dark ink on a white background gives the clearest signal to the model.
+- **Sharpness** — avoid motion blur or out-of-focus shots.
+
+### Formula Complexity
+
+Simple single-line equations are recognized with near-perfect accuracy. More complex structures may have occasional errors:
+
+- Multi-line equation systems
+- Large matrices (6×6 or larger)
+- Heavily nested fractions (3+ levels deep)
+- Non-standard notation or custom symbols
+
+### Handwriting Style
+
+Printed (typed) formulas outperform handwritten ones, but TexPixel handles handwriting well when:
+
+- Letters are clearly formed and not connected (print style, not cursive)
+- Variables are written in distinct sizes (clearly different x and × for example)
+- Spacing between symbols is consistent
+
+### What Reduces Accuracy
+
+- **Rotated images** — formulas at an angle are harder to parse
+- **Overlapping elements** — crossed-out work, annotations, or arrows near symbols
+- **Pencil on paper** — low contrast; try increasing image brightness/contrast before uploading
+- **Multiple formulas in one image** — crop to the specific formula you need
+- **Decorative fonts** — calligraphic or stylized mathematical writing
+
+## Improving Results
+
+If you're getting errors, try these steps in order:
+
+1. **Increase image resolution** — scan at 300 DPI instead of 150 DPI
+2. **Improve contrast** — use a photo editor to increase brightness and contrast
+3. **Crop tightly** — remove surrounding text and whitespace
+4. **Straighten the image** — correct rotation before uploading
+5. **Re-photograph** — better lighting, closer distance, sharper focus
+
+## Reporting Errors
+
+Found a formula type that TexPixel consistently gets wrong? Let us know — accuracy feedback directly improves the model over time.
+
+Contact us at: [support@texpixel.com](mailto:support@texpixel.com)
+
+---
+
+[Upload a formula and test accuracy →](/app)

content/docs/en/pdf-extraction.md

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+---
+title: PDF Extraction
+description: Extract and convert formulas from PDF documents automatically with TexPixel
+slug: pdf-extraction
+date: 2026-03-25
+tags: [PDF, extraction]
+order: 6
+---
+
+# PDF Extraction
+
+TexPixel can process entire PDF documents and extract every formula from every page — automatically. This is useful for textbooks, research papers, or any multi-page document with mathematical content.
+
+## How to Extract from a PDF
+
+1. Click the upload zone or drag and drop your PDF file.
+2. TexPixel detects all pages and identifies formula regions.
+3. Each recognized formula is listed in the result panel.
+4. Copy individual formulas or export the entire document as DOCX.
+
+## What Gets Extracted
+
+TexPixel identifies formulas in PDFs regardless of whether they were:
+- Typeset in LaTeX (rendered as vector math)
+- Embedded as images (scanned pages)
+- A mix of both
+
+For vector PDFs (generated from LaTeX or Word), recognition accuracy is typically 95%+. For scanned/image PDFs, accuracy follows the same image quality guidelines as regular image uploads.
+
+## Supported PDF Types
+
+| Type | Description | Accuracy |
+|---|---|---|
+| Vector PDF | Created from LaTeX, Word, or typesetting tools | 95–99% |
+| Scanned PDF (high quality) | 300 DPI scan of printed text | 90–97% |
+| Scanned PDF (low quality) | < 150 DPI or poor contrast | 60–80% |
+| Photo PDF | Photographed pages embedded as images | 75–90% |
+
+## File Limits
+
+- **Max file size:** 20 MB
+- **Max pages:** 50 pages per upload (Pro plan: unlimited)
+- **Processing time:** ~2–5 seconds per page
+
+For documents exceeding these limits, split the PDF into smaller chunks before uploading.
+
+## Exporting PDF Results
+
+After extraction, you can export in several ways:
+
+- **Copy individual formula** — click any recognized formula to copy its LaTeX
+- **DOCX export** — download the full document with formulas as native Word equations
+- **Batch copy** — copy all formulas as a list (Pro feature)
+
+## Tips for Better PDF Results
+
+- **Use the original PDF**, not a re-scanned copy — vector PDFs give the best results
+- **Avoid password-protected PDFs** — these cannot be processed
+- **Crop pages** if a PDF has wide margins with no content — smaller pages process faster
+- **Split by chapter** for very large documents to stay within page limits
+
+## Common Issues
+
+**"No formulas found"**
+The PDF may be encrypted, have formulas stored as complex vector paths, or use non-standard encoding. Try converting the page to a PNG image and uploading that instead.
+
+**Formulas recognized but garbled**
+This often happens with very low DPI scans. Try using a PDF scanner app to rescan at 300 DPI before uploading.
+
+**Processing is slow**
+Large PDFs with many pages can take 30–60 seconds. This is normal. The result will appear when processing is complete.
+
+---
+
+[Upload a PDF and extract formulas →](/app)