feat: expandable previews, KaTeX rendering, variant speedup, batch import

- Analytics/Similar: expandable question preview with KaTeX rendering
- KaTeXRenderer: auto markdown-to-HTML (code blocks, tables, bold), auto Unicode→LaTeX
- ErrorBook: full question text rendering instead of truncated preview
- Variant: remove hint/solution from generation (faster), async, fix null crash
- Grading: add max_tokens limit
- JSON parser: robust multi-layer repair + JSONDecodeError retry
- Extraction prompt: enforce LaTeX notation for math
- Upload: redirect to home instead of blank paper page
- ProcessingBanner: add ETA time estimate + percentage
- Batch import script + handoff guide for team

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/services/paper_processor.py

@@ -35,6 +35,8 @@ CRITICAL RULES for question_text:
 - For sub-questions (e.g. (a)(i)), copy the ENTIRE parent question setup (variable definitions, code blocks, problem description) into the question_text, then append the specific sub-question.
 - For Python/code questions: include ALL variable definitions and import statements verbatim, exactly as they appear in the exam, preserving multi-line arrays and data structures completely.
 - Never truncate code. If a variable is defined across multiple lines (e.g. a numpy array), include every line.
+- CRITICAL: ALL mathematical expressions, formulas, variables, and symbols MUST use LaTeX notation. Wrap inline math with $...$ and display math with $$...$$. NEVER use Unicode symbols like σ, μ, π, ², ≥, ≤, √, ∑, etc. Use $\sigma$, $\mu$, $\pi$, $^2$, $\geq$, $\leq$, $\sqrt{}$, $\sum$, etc. Every fraction should be $\frac{a}{b}$, every subscript $x_i$, every superscript $x^n$.
+- Code blocks must use markdown fenced code blocks (```python ... ```).
 
 Output JSON format (strictly follow):
 {
@@ -203,6 +205,8 @@ RETRYABLE_ERROR_MARKERS = (
 
 
 def is_retryable_error(exc: Exception) -> bool:
+    if isinstance(exc, json.JSONDecodeError):
+        return True  # LLM returned bad JSON, retry may fix it
     message = str(exc).lower()
     return any(marker in message for marker in RETRYABLE_ERROR_MARKERS)
 
@@ -221,17 +225,51 @@ def pdf_to_images(pdf_bytes: bytes, dpi: int = 96) -> list[str]:
 
 
 def parse_json_response(text: str) -> dict:
-    """解析模型返回的 JSON，兼容 markdown 代码块包装"""
+    """解析模型返回的 JSON，兼容各种格式问题"""
     text = text.strip()
-    # 去掉 ```json ... ``` 包装
+
+    # 1. 去掉 ```json ... ``` 包装
     if text.startswith("```"):
         lines = text.splitlines()
         text = "\n".join(lines[1:-1] if lines[-1].strip() == "```" else lines[1:])
-    # 移除 JSON 字符串中的非法控制字符（0x00-0x1F 除了 \t \n \r）
+
+    # 2. 如果不以 { 开头，尝试找到第一个 {
+    idx = text.find("{")
+    if idx > 0:
+        text = text[idx:]
+    # 找到最后一个 } 截断尾部垃圾
+    ridx = text.rfind("}")
+    if ridx > 0:
+        text = text[:ridx + 1]
+
+    # 3. 移除所有非法控制字符（0x00-0x1F 除了 \t \n \r）
     text = re.sub(r'[\x00-\x08\x0b\x0c\x0e-\x1f]', '', text)
-    # 修复模型返回的无效 JSON 转义序列：只修奇数个反斜杠后的非法字符
-    text = re.sub(r'(?<!\\)((?:\\\\)*)\\([^"\\/bfnrtu])', r'\1\\\\\2', text)
-    return json.loads(text)
+
+    # 4. 修复无效 JSON 转义：LaTeX 如 \sqrt, \sigma 等
+    text = re.sub(r'(?<!\\)((?:\\\\)*)\\([^"\\/bfnrtu\n])', r'\1\\\\\2', text)
+
+    # 5. 尝试解析
+    try:
+        return json.loads(text)
+    except json.JSONDecodeError:
+        pass
+
+    # 6. 更激进的修复：移除所有控制字符包括 \t
+    text = re.sub(r'[\x00-\x1f]', lambda m: ' ' if m.group() in '\t\n\r' else '', text)
+
+    # 7. 修复未终止的字符串：在行尾补引号
+    text = re.sub(r'(?<!\\)"([^"]*)\n', r'"\1\\n"\n', text)
+
+    try:
+        return json.loads(text)
+    except json.JSONDecodeError:
+        pass
+
+    # 8. 最后一搏：用 strict=False 解析
+    try:
+        return json.loads(text, strict=False)
+    except json.JSONDecodeError:
+        raise
 
 
 async def gemini_vision_json(