Fix left-side gutter detection: find peak instead of scanning from edge

Left-side book fold shadows have a V-shape: brightness dips from the
edge toward a peak at ~5-10% of width, then rises again. The previous
algorithm scanned from the edge inward and immediately found a low
dark fraction (0.13 at x=0), missing the gutter entirely.

Now finds the PEAK of the dark fraction profile first, then scans from
that peak toward the page center to find the transition point. Works
for both V-shaped left gutters and edge-darkening right gutters.

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

klausur-service/backend/page_crop.py

@@ -535,19 +535,30 @@ def _detect_gutter_continuity(
     if region_w <= 2 * margin + 10:
         return None
 
-    # Scan from edge inward to find where frac drops below transition threshold
+    # Find the peak of dark fraction (gutter center).
+    # For right gutters the peak is near the edge; for left gutters
+    # (V-shaped spine shadow) the peak may be well inside the region.
     transition_thresh = 0.50
+    peak_frac = float(np.max(frac_smooth[margin:region_w - margin]))
+
+    if peak_frac < 0.70:
+        logger.debug(
+            "%s gutter: peak dark fraction %.2f < 0.70", side.capitalize(), peak_frac,
+        )
+        return None
+
+    peak_x = int(np.argmax(frac_smooth[margin:region_w - margin])) + margin
     gutter_inner = None  # local x in search_region
 
     if side == "right":
-        # Scan from right edge (region_w - 1) inward (toward 0)
-        for x in range(region_w - 1 - margin, margin, -1):
+        # Scan from peak toward the page center (leftward)
+        for x in range(peak_x, margin, -1):
             if frac_smooth[x] < transition_thresh:
-                gutter_inner = x + 1  # crop just past the transition
+                gutter_inner = x + 1
                 break
     else:
-        # Scan from left edge (0) inward (toward region_w)
-        for x in range(margin, region_w - margin):
+        # Scan from peak toward the page center (rightward)
+        for x in range(peak_x, region_w - margin):
             if frac_smooth[x] < transition_thresh:
                 gutter_inner = x - 1
                 break