Fix analysis display for recipe-based runs

Add get_run_analysis() to RunService to load per-input analysis from
CACHE_DIR/analysis/{hash}.json files. Update runs router and template
to display tempo, beats, energy, and beat timeline visualization.

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

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

app/services/run_service.py

@@ -225,3 +225,43 @@ class RunService:
                     artifacts.append(info)
 
         return artifacts
+
+    async def get_run_analysis(self, run_id: str) -> List[Dict[str, Any]]:
+        """Get analysis data for each input in a run."""
+        from pathlib import Path
+        import os
+
+        run = await self.get_run(run_id)
+        if not run:
+            return []
+
+        cache_dir = Path(os.environ.get("CACHE_DIR", "/tmp/artdag-cache"))
+        analysis_dir = cache_dir / "analysis"
+
+        results = []
+        inputs = run.get("inputs", [])
+        if isinstance(inputs, dict):
+            inputs = list(inputs.values())
+
+        for i, input_hash in enumerate(inputs):
+            analysis_path = analysis_dir / f"{input_hash}.json"
+            analysis_data = None
+
+            if analysis_path.exists():
+                try:
+                    with open(analysis_path) as f:
+                        analysis_data = json.load(f)
+                except (json.JSONDecodeError, IOError):
+                    pass
+
+            results.append({
+                "input_hash": input_hash,
+                "input_name": f"Input {i + 1}",
+                "has_analysis": analysis_data is not None,
+                "tempo": analysis_data.get("tempo") if analysis_data else None,
+                "beat_times": analysis_data.get("beat_times", []) if analysis_data else [],
+                "energy": analysis_data.get("energy") if analysis_data else None,
+                "raw": analysis_data,
+            })
+
+        return results