fix(sub-columns): convert relative word positions to absolute coords for split

Word 'left' values in ColumnGeometry.words are relative to the content
ROI (left_x), but geo.x is in absolute image coordinates. The split
position was computed from relative word positions and then compared
against absolute geo.x, resulting in negative widths and no splits on
real data. Pass left_x through to _detect_sub_columns to bridge the
two coordinate systems.

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

klausur-service/backend/cv_vocab_pipeline.py

@@ -1037,6 +1037,7 @@ def _detect_columns_by_clustering(
 def _detect_sub_columns(
     geometries: List[ColumnGeometry],
     content_w: int,
+    left_x: int = 0,
     _edge_tolerance: int = 8,
     _min_col_start_ratio: float = 0.10,
 ) -> List[ColumnGeometry]:
@@ -1048,6 +1049,10 @@ def _detect_sub_columns(
     start.  Any words to the left of that bin form a sub-column, provided they
     number >= 2 and < 35 % of total.
 
+    Word ``left`` values are relative to the content ROI (offset by *left_x*),
+    while ``ColumnGeometry.x`` is in absolute image coordinates.  *left_x*
+    bridges the two coordinate systems.
+
     Returns a new list of ColumnGeometry — potentially longer than the input.
     """
     if content_w <= 0:
@@ -1101,13 +1106,16 @@ def _detect_sub_columns(
             continue
 
         # --- Build two sub-column geometries ---
+        # Word 'left' values are relative to left_x; geo.x is absolute.
+        # Convert the split position from relative to absolute coordinates.
         max_sub_left = max(w['left'] for w in sub_words)
-        split_x = (max_sub_left + col_start_bin[2]) // 2
+        split_rel = (max_sub_left + col_start_bin[2]) // 2
+        split_abs = split_rel + left_x
 
         sub_x = geo.x
-        sub_width = split_x - geo.x
-        main_x = split_x
-        main_width = (geo.x + geo.width) - split_x
+        sub_width = split_abs - geo.x
+        main_x = split_abs
+        main_width = (geo.x + geo.width) - split_abs
 
         if sub_width <= 0 or main_width <= 0:
             result.append(geo)
@@ -1138,8 +1146,9 @@ def _detect_sub_columns(
         result.append(main_geo)
 
         logger.info(
-            f"SubColumnSplit: column idx={geo.index} split at x={split_x}, "
-            f"sub={len(sub_words)} words (left), main={len(main_words)} words, "
+            f"SubColumnSplit: column idx={geo.index} split at abs_x={split_abs} "
+            f"(rel={split_rel}), sub={len(sub_words)} words, "
+            f"main={len(main_words)} words, "
             f"col_start_bin=({col_start_bin[0]}, n={col_start_bin[1]})"
         )
 
@@ -2846,7 +2855,7 @@ def analyze_layout_by_words(ocr_img: np.ndarray, dewarped_bgr: np.ndarray) -> Li
     content_w = right_x - left_x
 
     # Split sub-columns (e.g. page references) before classification
-    geometries = _detect_sub_columns(geometries, content_w)
+    geometries = _detect_sub_columns(geometries, content_w, left_x=left_x)
 
     # Phase B: Content-based classification
     regions = classify_column_types(geometries, content_w, top_y, w, h, bottom_y,