docs: update project documentation and verification strategies

- Update GEMINI.md with verification steps and remove ignored docs reference
- Update README.md to remove reference to local langchain-docs
- Update backend/GEMINI.md with correct database schema (users table) and architecture details
- Update frontend/GEMINI.md with latest project structure

GEMINI.md

@@ -43,9 +43,22 @@ The frontend is a modern SPA (Single Page Application) designed for data-heavy i
 - **Real-time Visualization**: Supports streaming text responses and immediate rendering of base64-encoded or binary-retrieved analysis plots.
 
 ## Documentation
+- **[README](./README.md)**: Main project documentation and setup guide.
 - **[Backend Guide](./backend/GEMINI.md)**: Detailed information about the backend architecture, migration goals, and implementation steps.
 - **[Frontend Guide](./frontend/GEMINI.md)**: Frontend development guide and technology stack.
-- **LangChain Docs**: See the `langchain-docs/` folder for local LangChain and LangGraph documentation.
+
+## Verification Strategy
+When making changes, always verify using the following commands:
+
+### Backend
+- **Test**: `cd backend && uv run pytest`
+- **Lint/Format**: `cd backend && uv run ruff check .`
+- **Type Check**: `cd backend && uv run mypy .` (if configured)
+
+### Frontend
+- **Test**: `cd frontend && npm run test`
+- **Lint**: `cd frontend && npm run lint`
+- **Build**: `cd frontend && npm run build` (to ensure no compilation errors)
 
 ## Git Operations
 - All new feature and bug-fix branches must be created from the `develop` branch except hot-fix.