feat: Major update with validators, skills, dashboard, and docs reorganization

- Add validation framework (config, model, results, study validators)
- Add Claude Code skills (create-study, run-optimization, generate-report,
  troubleshoot, analyze-model)
- Add Atomizer Dashboard (React frontend + FastAPI backend)
- Reorganize docs into structured directories (00-09)
- Add neural surrogate modules and training infrastructure
- Add multi-objective optimization support

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

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

atomizer-dashboard/backend/api/routes/optimization.py

@@ -337,11 +337,18 @@ async def get_optimization_history(study_id: str, limit: Optional[int] = None):
                 if not results and len(values) > 0:
                     results["first_frequency"] = values[0]
 
+                # CRITICAL: Extract design_vars from user_attrs if stored there
+                # The optimization code does: trial.set_user_attr("design_vars", design_vars)
+                design_vars_from_attrs = user_attrs.get("design_vars", {})
+
+                # Merge with params (prefer user_attrs design_vars if available)
+                final_design_vars = {**params, **design_vars_from_attrs} if design_vars_from_attrs else params
+
                 trials.append({
                     "trial_number": trial_num,
                     "objective": values[0] if len(values) > 0 else None,  # Primary objective
                     "objectives": values if len(values) > 1 else None,  # All objectives for multi-objective
-                    "design_variables": params,
+                    "design_variables": final_design_vars,  # Use merged design vars
                     "results": results,
                     "user_attrs": user_attrs,  # Include all user attributes
                     "start_time": start_time,
@@ -679,6 +686,53 @@ async def get_mesh_file(study_id: str, filename: str):
     except Exception as e:
         raise HTTPException(status_code=500, detail=f"Failed to serve mesh file: {str(e)}")
 
+@router.get("/studies/{study_id}/optuna-url")
+async def get_optuna_dashboard_url(study_id: str):
+    """
+    Get the Optuna dashboard URL for a specific study.
+    Returns the URL to access the study in Optuna dashboard.
+
+    The Optuna dashboard should be started with a relative path from the Atomizer root:
+    sqlite:///studies/{study_id}/2_results/study.db
+    """
+    try:
+        study_dir = STUDIES_DIR / study_id
+        if not study_dir.exists():
+            raise HTTPException(status_code=404, detail=f"Study {study_id} not found")
+
+        results_dir = study_dir / "2_results"
+        study_db = results_dir / "study.db"
+
+        if not study_db.exists():
+            raise HTTPException(status_code=404, detail=f"No Optuna database found for study {study_id}")
+
+        # Get the study name from the database (may differ from folder name)
+        import optuna
+        storage = optuna.storages.RDBStorage(f"sqlite:///{study_db}")
+        studies = storage.get_all_studies()
+
+        if not studies:
+            raise HTTPException(status_code=404, detail=f"No Optuna study found in database for {study_id}")
+
+        # Use the actual study name from the database
+        optuna_study_name = studies[0].study_name
+
+        # Return URL info for the frontend
+        # The dashboard should be running on port 8081 with the correct database
+        return {
+            "study_id": study_id,
+            "optuna_study_name": optuna_study_name,
+            "database_path": f"studies/{study_id}/2_results/study.db",
+            "dashboard_url": f"http://localhost:8081/dashboard/studies/{studies[0]._study_id}",
+            "dashboard_base": "http://localhost:8081",
+            "note": "Optuna dashboard must be started with: sqlite:///studies/{study_id}/2_results/study.db"
+        }
+
+    except FileNotFoundError:
+        raise HTTPException(status_code=404, detail=f"Study {study_id} not found")
+    except Exception as e:
+        raise HTTPException(status_code=500, detail=f"Failed to get Optuna URL: {str(e)}")
+
 @router.post("/studies/{study_id}/generate-report")
 async def generate_report(
     study_id: str,