feat: dynamic pause point buffer based on gap duration

Instead of a fixed 175ms buffer, the pause point is now placed
halfway between the end of the sentence and the start of the
next word. If the half-gap exceeds 2 seconds, uses 500ms instead.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/services/whisper_service.py

@@ -219,9 +219,21 @@ class WhisperService:
 
         best_gap = candidate_gaps[0]
 
-        # Use gap.start (end of previous sentence) as the pause point
-        # Add buffer (175ms) to ensure the sentence is fully heard
-        refined = best_gap.start + 0.175
+        # Calculate buffer: halfway between end of sentence and start of next word,
+        # unless that would be more than 2 seconds, in which case use 500ms
+        half_gap = best_gap.duration / 2
+        if half_gap > 2.0:
+            buffer = 0.5
+        else:
+            buffer = half_gap
+
+        # Use gap.start (end of previous sentence) + buffer as the pause point
+        refined = best_gap.start + buffer
+
+        logger.debug(
+            f"Pause point buffer: gap_duration={best_gap.duration:.3f}s, "
+            f"half_gap={half_gap:.3f}s, buffer_used={buffer:.3f}s"
+        )
 
         return refined, None
 
@@ -347,8 +359,8 @@ class WhisperService:
     def _find_gap_type(self, timestamp: float, gaps: list[SpeechGap]) -> str:
         """Find the gap type for a given timestamp."""
         for gap in gaps:
-            # Check if timestamp matches gap.start + 175ms buffer
-            if abs(gap.start + 0.175 - timestamp) < 0.01:
+            # Check if timestamp falls within this gap (between end of prev word and start of next)
+            if gap.start <= timestamp <= gap.end:
                 return gap.gap_type
         return "unknown"