feat: add rm fake title

app/services/ocr_service.py

@@ -272,7 +272,87 @@ def _postprocess_markdown(markdown_content: str) -> str:
             return f"${_postprocess_math(seg[1:-1])}$"
         return seg
 
-    return _MATH_SEGMENT_PATTERN.sub(_fix_segment, markdown_content)
+    markdown_content = _MATH_SEGMENT_PATTERN.sub(_fix_segment, markdown_content)
+    
+    # Apply markdown-level postprocessing (after LaTeX processing)
+    markdown_content = _remove_false_heading_from_single_formula(markdown_content)
+    
+    return markdown_content
+
+
+def _remove_false_heading_from_single_formula(markdown_content: str) -> str:
+    """Remove false heading markers from single-formula content.
+    
+    OCR sometimes incorrectly identifies a single formula as a heading by adding '#' prefix.
+    This function detects and removes the heading marker when:
+    1. The content contains only one formula (display or inline)
+    2. The formula line starts with '#' (heading marker)
+    3. No other non-formula text content exists
+    
+    Examples:
+        Input:  "# $$E = mc^2$$"
+        Output: "$$E = mc^2$$"
+        
+        Input:  "# $x = y$"
+        Output: "$x = y$"
+        
+        Input:  "# Introduction\n$$E = mc^2$$"  (has text, keep heading)
+        Output: "# Introduction\n$$E = mc^2$$"
+    
+    Args:
+        markdown_content: Markdown text with potential false headings.
+        
+    Returns:
+        Markdown text with false heading markers removed.
+    """
+    if not markdown_content or not markdown_content.strip():
+        return markdown_content
+    
+    lines = markdown_content.split('\n')
+    
+    # Count formulas and heading lines
+    formula_count = 0
+    heading_lines = []
+    has_non_formula_text = False
+    
+    for i, line in enumerate(lines):
+        line_stripped = line.strip()
+        
+        if not line_stripped:
+            continue
+        
+        # Check if line starts with heading marker
+        heading_match = re.match(r'^(#{1,6})\s+(.+)$', line_stripped)
+        
+        if heading_match:
+            heading_level = heading_match.group(1)
+            content = heading_match.group(2)
+            
+            # Check if the heading content is a formula
+            if re.fullmatch(r'\$\$?.+\$\$?', content):
+                # This is a heading with a formula
+                heading_lines.append((i, heading_level, content))
+                formula_count += 1
+            else:
+                # This is a real heading with text
+                has_non_formula_text = True
+        elif re.fullmatch(r'\$\$?.+\$\$?', line_stripped):
+            # Standalone formula line (not in a heading)
+            formula_count += 1
+        elif line_stripped and not re.match(r'^#+\s*$', line_stripped):
+            # Non-empty, non-heading, non-formula line
+            has_non_formula_text = True
+    
+    # Only remove heading markers if:
+    # 1. There's exactly one formula
+    # 2. That formula is in a heading line
+    # 3. There's no other text content
+    if formula_count == 1 and len(heading_lines) == 1 and not has_non_formula_text:
+        # Remove the heading marker from the formula
+        line_idx, heading_level, formula_content = heading_lines[0]
+        lines[line_idx] = formula_content
+    
+    return '\n'.join(lines)
 
 
 class OCRServiceBase(ABC):