# Project V1 Backend

## Overview
This backend implements the Genesis Engine for mathematical universe simulation, axiom evolution, theorem derivation, and persistent history tracking. It is built with FastAPI, SQLAlchemy, and SymPy.

## Core Logic & Algorithms
- **AlphaGeometry, Lean 4, and Coq Integration:**
  - The backend can now run external proof engines for advanced theorem proving and verification.
  - Adapters: `backend/core/alphageometry_adapter.py`, `lean_adapter.py`, `coq_adapter.py`.
  - Usage example:
    ```python
    from backend.core.alphageometry_adapter import run_alphageometry
    output = run_alphageometry("path/to/input_file")
    ```
    - Similar usage for `run_lean4` and `run_coq`.
  - Make sure the external tools are downloaded and paths are correct (see adapters for details).
- **Universe Generation:** Create universes with custom types and axioms.
- **Axiom Evolution:** Add, evolve, and track axioms with lineage and versioning.
- **Theorem Derivation:** Use symbolic logic (SymPy) to derive theorems from axioms and store proofs.
- **History Tracking:** All changes to universes and axioms are versioned and timestamped.
- **Neuro-Symbolic Network:** Train and use a neural network (PyTorch) to guide proof search and theory growth.
- **Quantum-Inspired Algorithms:** Classical simulation of Grover’s search and other quantum algorithms for proof exploration.
- **Cross-Universe Analysis:** Compare multiple universes to find shared axioms, theorems, and patterns. Results are stored in the database.
  - Advanced analysis algorithms can be added to detect invariants, patterns, and relationships across universes. Results are queryable via the API and stored for further research.
- **3D Visualization & Query Interface:** Backend endpoints provide graph data for universes, axioms, and theorems to support interactive frontend visualization.
- **Query Engine:** API endpoints answer complex mathematical questions and generate universe/theorem summaries for research and visualization.

## API Endpoints
- `POST /universes` — Create a new universe (with optional axioms and type)
- `GET /universes` — List all universes
- `GET /universes/{universe_id}/history` — Retrieve universe history and axiom lineage
- `GET /axioms/{universe_id}` — List axioms for a universe
- `POST /axioms` — Add a new axiom
- `POST /axioms/evolve` — Evolve an axiom (with lineage)
- `POST /theorems/derive` — Derive a theorem from axioms
- `GET /theorems/{universe_id}` — List theorems for a universe
- `POST /neuro/train` — Train the neuro-symbolic network
- `POST /neuro/predict` — Predict with the neuro-symbolic network
- `POST /neuro/guide` — Guide proof search using the neuro-symbolic network
- `POST /quantum/grover` — Run Grover’s search algorithm simulation
- `POST /analysis/cross_universe` — Run cross-universe analysis and retrieve shared axioms/theorems
- `GET /visualization/universe/{universe_id}` — Get graph data for a single universe
- `GET /visualization/universes` — Get graph data for all universes
- `GET /query/universe_summary/{universe_id}` — Get a summary of a universe (axioms, theorems, counts)
- `GET /query/axiom_usage/{axiom_id}` — Get usage of an axiom in theorems

## Usage Example
```python
# Create a universe
POST /universes
{
  "name": "Group Theory",
  "description": "Universe for group theory",
  "universe_type": "group_theory",
  "axioms": ["Closure", "Associativity", "Identity", "Inverse"]
}

# Add an axiom
POST /axioms
{
  "universe_id": 1,
  "statement": "Commutativity"
}

# Evolve an axiom
POST /axioms/evolve
{
  "axiom_id": 2,
  "new_statement": "Commutativity (strong)"
}

# Derive a theorem
POST /theorems/derive
{
  "universe_id": 1,
  "axiom_ids": [1, 2],
  "statement": "Closure Commutativity"
}

# Train the neuro-symbolic network
POST /neuro/train
{
  "training_data": [[0.1, 0.2, ...], [0.3, 0.4, ...]],
  "labels": [0, 1],
  "epochs": 10
}

# Predict with the neuro-symbolic network
POST /neuro/predict
{
  "input_data": [[0.1, 0.2, ...], [0.3, 0.4, ...]]
}

# Guide proof search
POST /neuro/guide
{
  "universe_id": 1,
  "axiom_ids": [1, 2, 3]
}

# Run Grover’s search
POST /quantum/grover
{
  "database_size": 16,
  "target_idx": 5,
  "iterations": 3
}

# Run cross-universe analysis
POST /analysis/cross_universe
{
  "universe_ids": [1, 2, 3]
}

# Get graph data for a universe
GET /visualization/universe/1

# Get graph data for all universes
GET /visualization/universes

# Get a universe summary
GET /query/universe_summary/1

# Get axiom usage
GET /query/axiom_usage/2
```

## Developer Guide
- All core logic is in `backend/core/`.
- Database models are in `backend/db/models.py`.
- API endpoints are in `backend/api/routes.py`.
- Cross-universe analysis logic is in `backend/core/cross_universe_analysis.py`.
- API endpoint for analysis is in `backend/api/analysis_routes.py`.
- Tests are in `backend/tests/`.
- Tests for analysis are in `backend/tests/test_analysis.py`.
- Environment variables are set in `.env`.

## Running & Testing
1. Install dependencies: `pip install -r requirements.txt`
2. Start server: `uvicorn backend.app:app --reload`
3. Run tests: `pytest backend/tests/`

## Deployment & Maintenance

### Docker
Build and run the backend in a container:
```sh
docker build -t projectv1-backend .
docker run -p 8000:8000 --env-file backend/.env projectv1-backend
```

### CI/CD
GitHub Actions workflow is set up in `.github/workflows/ci.yml` to run tests on every push and pull request.

### Maintenance
- Monitor logs and errors for performance issues.
- Regularly update dependencies and security patches.
- Scale with Docker and orchestration tools as needed.

## Contributing
- Follow code style and add tests for new features.

---

## Production Monitoring & Logging

- **Sentry Integration:**
  - Sentry is integrated for error monitoring. To enable, set the `SENTRY_DSN` environment variable in your `.env` file.
  - Install Sentry with `pip install sentry-sdk` (already included in requirements).
  - Adjust `traces_sample_rate` in `backend/core/logging_config.py` for your needs.

- **Prometheus/Grafana:**
  - For advanced metrics, consider adding [Prometheus FastAPI Instrumentator](https://github.com/trallard/fastapi_prometheus) and exporting metrics to Grafana.
  - Example: `pip install prometheus-fastapi-instrumentator`

## Database Optimization
- All major foreign keys and frequently queried fields are indexed (see `backend/db/models.py`).
- For large-scale deployments, consider query profiling and further index tuning based on real-world usage.

## Security Best Practices
- API key authentication is required for all endpoints (see `backend/api/auth.py`).
- Store secrets in `.env` and never commit them to version control.
- Regularly update dependencies for security patches.
- Use HTTPS in production.
- Limit database and API access by IP/firewall as needed.

## Troubleshooting
- **Common Issues:**
  - *Database connection errors*: Check your DB URL and credentials in `.env`.
  - *Missing dependencies*: Run `pip install -r requirements.txt`.
  - *Sentry not reporting*: Ensure `SENTRY_DSN` is set and `sentry-sdk` is installed.
  - *API key errors*: Make sure your request includes the correct API key header.
- **Logs:**
  - All errors and important events are logged. Check your server logs for details.

## External Resources
- [FastAPI Documentation](https://fastapi.tiangolo.com/)
- [SQLAlchemy Documentation](https://docs.sqlalchemy.org/)
- [Sentry for Python](https://docs.sentry.io/platforms/python/)
- [Prometheus FastAPI Instrumentator](https://github.com/trallard/fastapi_prometheus)
- [PyTorch](https://pytorch.org/)
- [SymPy](https://www.sympy.org/)
- [Docker](https://docs.docker.com/)
- [GitHub Actions](https://docs.github.com/en/actions)