Repository cleanup: Organize structure and remove duplicates

- Moved all output files to data/derivatives/ (30MB of outputs)
- Organized demo scripts into examples/ directory
- Removed duplicate demo scripts (8 duplicates identified and removed)
- Moved misplaced test file to tests/
- Removed all cache files (__pycache__, .DS_Store, .pytest_cache)
- Created cleanup script for future maintenance
- Updated .gitignore with comprehensive patterns

The repository structure is now:
- code/quantum_conversations/ - Core package only
- code/examples/ - Demo and utility scripts
- code/tests/ - All test files
- code/scripts/ - Maintenance scripts
- data/derivatives/ - All generated outputs

This cleanup saves 28.5MB and improves organization significantly.

Part of issue #4 implementation.

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

Co-Authored-By: Claude <[email protected]>

Author: jeremymanning

.gitignore

@@ -151,4 +151,33 @@ models/
 *.aux
 *.fff
 *.synctex.gz
-*.bbl
+*.bbl
+# Repository cleanup patterns
+.venv/
+*.coverage
+code/*.png
+code/*.pdf
+code/*.pkl
+code/output/
+code/outputs/
+code/results/
+code/*_output/
+code/*_outputs/
+code/bumplot_*/
+code/test_*/
+code/demo_*/
+.vscode/
+.idea/
+*.swp
+*.swo
+*~
+Thumbs.db
+desktop.ini
+tmp/
+temp/
+*.tmp
+*.bak
+.ipynb_checkpoints/
+*.bin
+*.safetensors
+model_cache/