diff --git a/app/services/glm_postprocess.py b/app/services/glm_postprocess.py
index d84e589..36256fd 100644
--- a/app/services/glm_postprocess.py
+++ b/app/services/glm_postprocess.py
@@ -13,8 +13,11 @@ Covers:
 
 from __future__ import annotations
 
+import logging
 import re
 import json
+
+logger = logging.getLogger(__name__)
 from collections import Counter
 from copy import deepcopy
 from typing import Any, Dict, List, Optional, Tuple
@@ -94,8 +97,18 @@ def clean_repeated_content(
 
 
 def clean_formula_number(number_content: str) -> str:
-    """Strip parentheses from a formula number string, e.g. '(1)' → '1'."""
+    """Strip delimiters from a formula number string, e.g. '(1)' → '1'.
+
+    Also strips math-mode delimiters ($$, $, \\[...\\]) that vLLM may add
+    when the region is processed with a formula prompt.
+    """
     s = number_content.strip()
+    # Strip display math delimiters
+    for start, end in [("$$", "$$"), (r"\[", r"\]"), ("$", "$"), (r"\(", r"\)")]:
+        if s.startswith(start) and s.endswith(end) and len(s) > len(start) + len(end):
+            s = s[len(start):-len(end)].strip()
+            break
+    # Strip CJK/ASCII parentheses
     if s.startswith("(") and s.endswith(")"):
         return s[1:-1]
     if s.startswith("（") and s.endswith("）"):
@@ -253,6 +266,9 @@ class GLMResultFormatter:
                 if content.startswith(s) and content.endswith(e):
                     content = content[len(s) : -len(e)].strip()
                     break
+            if not content:
+                logger.warning("Skipping formula region with empty content after stripping delimiters")
+                return ""
             content = "$$\n" + content + "\n$$"
 
         # Text formatting
diff --git a/app/services/layout_detector.py b/app/services/layout_detector.py
index 84b0647..36eb1b9 100644
--- a/app/services/layout_detector.py
+++ b/app/services/layout_detector.py
@@ -66,7 +66,9 @@ class LayoutDetector:
         # Formula types
         "display_formula": "formula",
         "inline_formula": "formula",
-        "formula_number": "formula",
+        # formula_number is a plain text annotation "(2.9)" next to a formula,
+        # not a formula itself — use text prompt so vLLM returns plain text
+        "formula_number": "text",
         # Table types
         "table": "table",
         # Figure types
diff --git a/app/services/ocr_service.py b/app/services/ocr_service.py
index 28de285..321a483 100644
--- a/app/services/ocr_service.py
+++ b/app/services/ocr_service.py
@@ -1,6 +1,7 @@
 """PaddleOCR-VL client service for text and formula recognition."""
 
 import base64
+import logging
 import re
 from abc import ABC, abstractmethod
 from concurrent.futures import ThreadPoolExecutor, as_completed
@@ -20,6 +21,7 @@ from app.services.image_processor import ImageProcessor
 from app.services.layout_detector import LayoutDetector
 
 settings = get_settings()
+logger = logging.getLogger(__name__)
 
 _COMMANDS_NEED_SPACE = {
     # operators / calculus
@@ -883,6 +885,9 @@ class GLMOCREndToEndService(OCRServiceBase):
         # 2. Layout detection
         layout_info = self.layout_detector.detect(padded)
 
+        # Sort regions in reading order: top-to-bottom, left-to-right
+        layout_info.regions.sort(key=lambda r: (r.bbox[1], r.bbox[0]))
+
         # 3. OCR: per-region (parallel) or full-image fallback
         if not layout_info.regions:
             raw_content = self._call_vllm(padded, _DEFAULT_PROMPT)
@@ -895,7 +900,13 @@ class GLMOCREndToEndService(OCRServiceBase):
                     continue
                 x1, y1, x2, y2 = (int(c) for c in region.bbox)
                 cropped = padded[y1:y2, x1:x2]
-                if cropped.size == 0:
+                if cropped.size == 0 or cropped.shape[0] < 10 or cropped.shape[1] < 10:
+                    logger.warning(
+                        "Skipping region idx=%d (label=%s): crop too small %s",
+                        idx,
+                        region.native_label,
+                        cropped.shape[:2],
+                    )
                     continue
                 prompt = _TASK_PROMPTS.get(region.type, _DEFAULT_PROMPT)
                 tasks.append((idx, region, cropped, prompt))
@@ -915,7 +926,8 @@ class GLMOCREndToEndService(OCRServiceBase):
                         idx = future_map[future]
                         try:
                             raw_results[idx] = future.result()
-                        except Exception:
+                        except Exception as e:
+                            logger.warning("vLLM call failed for region idx=%d: %s", idx, e)
                             raw_results[idx] = ""
 
                 # Build structured region dicts for GLMResultFormatter
@@ -940,8 +952,11 @@ class GLMOCREndToEndService(OCRServiceBase):
         # 6. Format conversion
         latex, mathml, mml = "", "", ""
         if markdown_content and self.converter:
-            fmt = self.converter.convert_to_formats(markdown_content)
-            latex, mathml, mml = fmt.latex, fmt.mathml, fmt.mml
+            try:
+                fmt = self.converter.convert_to_formats(markdown_content)
+                latex, mathml, mml = fmt.latex, fmt.mathml, fmt.mml
+            except RuntimeError as e:
+                logger.warning("Format conversion failed, returning empty latex/mathml/mml: %s", e)
 
         return {"markdown": markdown_content, "latex": latex, "mathml": mathml, "mml": mml}