feat: Enhance dashboard with charts, study report viewer, and pruning tracking

- Add ConvergencePlot component with running best, statistics, gradient fill
- Add ParameterImportanceChart with Pearson correlation analysis
- Add StudyReportViewer with KaTeX math rendering and full markdown support
- Update pruning endpoint to query Optuna database directly
- Add /report endpoint for STUDY_REPORT.md files
- Fix chart data transformation for single/multi-objective studies
- Update Protocol 13 documentation with new components
- Update generate-report skill with dashboard integration

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

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

.claude/skills/generate-report.md

@@ -1,7 +1,7 @@
 # Generate Report Skill
 
-**Last Updated**: November 25, 2025
-**Version**: 1.0 - Optimization Results Analysis and Reporting
+**Last Updated**: December 3, 2025
+**Version**: 1.1 - Optimization Results Analysis and Reporting (Dashboard Integration)
 
 You are helping the user understand and communicate optimization results.
 
@@ -390,6 +390,45 @@ Would you like me to:
 3. Continue optimization to explore more designs?
 ```
 
+## Dashboard Integration (December 2025)
+
+When a STUDY_REPORT.md file is generated, it can be viewed directly in the Atomizer Dashboard:
+
+1. **Save report to**: `studies/{study_name}/2_results/STUDY_REPORT.md`
+2. **View in dashboard**: Click "Study Report" button on the dashboard
+3. **Features**:
+   - Full markdown rendering with proper typography
+   - Math equation support via KaTeX (`$...$` inline, `$$...$$` block)
+   - Tables, code blocks, task lists
+   - Live refresh button for updates during analysis
+
+### Report Format for Dashboard
+
+Use standard markdown with optional LaTeX math:
+
+```markdown
+# Study Report: {study_name}
+
+## Summary
+
+The optimization achieved a **{improvement}%** improvement in objective.
+
+## Results
+
+| Trial | Objective | Improvement |
+|-------|-----------|-------------|
+| 0     | 100.0     | baseline    |
+| 10    | 85.5      | 14.5%       |
+
+## Mathematical Formulation
+
+The RMS wavefront error is calculated as:
+
+$$\text{RMS} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}c_i^2}$$
+
+where $c_i$ are the Zernike coefficients.
+```
+
 ## Notes
 
 - Reports should be actionable, not just data dumps
@@ -397,3 +436,4 @@ Would you like me to:
 - Consider the user's stated goals when highlighting results
 - Visualizations should be generated via Python scripts
 - Export formats should be compatible with common tools (Excel, etc.)
+- **Use STUDY_REPORT.md** for dashboard-viewable reports with math support