🚀 CRUX

The State-of-the-Art Intelligence

🌐 Who we are • 💬 Join Discord

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🧠 Breakthrough AI Research • 🎯 Mathematical Discovery • 🔬 Autonomous Problem Solving

🎓 Breakthrough Achievement: Revolutionary AI system demonstrating autonomous mathematical research and complex problem solving through hierarchical multi-agent orchestration.

⚡ Current Status: Open-sourced complete implementation including core Self-Evolve mechanism and production-ready web application.

• 9,000+ lines of internal reasoning
• 1+ hour of continuous problem-solving
• Complete mathematical proof with rigorous methodology

📄 View Solution - The final output showcasing Crux's unique approach to complex mathematical problems.

Starting from only the hypothesis, Crux autonomously derived:

• ✅ 9 systematic lemmas with complete mathematical rigor
• ✅ Full convergence proofs for the theoretical framework
• ✅ δ-bookkeeping methodology for practical implementation
• ✅ Research-grade theoretical foundations matching peer-reviewed standards
• 📄 View Research

• Hierarchical orchestration inspired by graduate school research structures
• Recursive depth capabilities for arbitrarily complex problems
• Dynamic specialist allocation based on problem complexity
• Proven scaling behavior similar to deep neural networks 📄 View Research - Complete independent mathematical derivation and analysis.

Paradigm Shift: Crux doesn't just reproduce existing work—it conducts original mathematical discovery through autonomous reasoning.

• Competition mathematics (USAMO, IMO level)
• Abstract algebra and number theory
• Combinatorics and graph theory
• Mathematical analysis and proofs

• Test-Time Reinforcement Learning (TTRL)
• Mathematical reasoning architectures
• Autonomous theorem proving
• AI-driven mathematical discovery

• Independent hypothesis verification
• Rigorous proof construction
• Systematic lemma development
• Mathematical framework derivation

Problem Solving Capability:

• Input: Mathematical problems, hypotheses, research questions
• Processing: 9,000+ lines of internal reasoning
• Output: Complete solutions with rigorous proofs
• Time: 1+ hours for complex problems

Research Methodology:

• Systematic lemma development
• Convergence proof construction
• Independent framework derivation
• Peer-reviewed quality standards

We welcome contributions to advancing AI-driven mathematical research! Feel free to:

• 🔬 Propose new mathematical challenges
• 📊 Share research insights and methodologies
• 🧮 Contribute to theoretical frameworks
• 📚 Help document research findings

• Current: Advanced mathematical reasoning and problem solving
• Q1 2025: Expanded theoretical framework development
• Q2 2025: Multi-domain mathematical applications
• Future: Revolutionary advances in AI-driven mathematical discovery

Our mission is to push the boundaries of AI-driven research and mathematical discovery. Crux represents a breakthrough in autonomous mathematical reasoning. Visit tooliense.com to learn more about our research initiatives.

The heart of Crux - implementing the IC-RL algorithm with enhanced multi-agent hierarchical architecture.

Key Features:

• Basic Self-Evolve mechanism (Generator → Evaluator → Refiner)
• Enhanced Professor-Specialist architecture
• Recursive deep agent hierarchies
• Dynamic function calling for optimal team composition

→ Read Full Documentation

Production-ready FastAPI + Next.js application for experiencing Crux capabilities.

Key Features:

• RESTful API with async processing (FastAPI + Celery)
• Modern React frontend with real-time updates
• Multi-provider LLM support (OpenAI, OpenRouter, DeepSeek)
• Supabase integration for authentication and persistence

→ Read Full Documentation

# Clone and setup
git clone https://github.com/your-org/crux.git
cd crux/self-evolve

# Install dependencies
pip install -r requirements.txt

# Set API keys
export OPENAI_API_KEY="your-key-here"

# Run basic example
python -m self-evolve.exampels.example_usage.py

# Run enhanced Professor-Graduate architecture
python -m self-evolve.examples.professor_graduate_example

# Navigate to agent directory
cd crux/crux-agent

# Setup backend
pip install -r requirements.txt
cp .env.example .env
# Edit .env with your API keys

# Start services
redis-server  # Terminal 1
python worker.py  # Terminal 2
uvicorn app.main:app --reload  # Terminal 3

# Setup frontend (new terminal)
cd crux-mvp
pnpm install
pnpm dev

Visit http://localhost:3000 to access the web interface.

• Treats prompts as trainable policy parameters
• Uses natural-language feedback as reward signals
• Achieves optimization through context refinement, not weight updates

🎓 Professor Agent
    ├── 🔬 Math Specialist → [Sub-specialists...]
    ├── 🔬 Logic Specialist → [Sub-specialists...]
    └── 🔬 Domain Specialist → [Sub-specialists...]

Each specialist can recursively become a professor, creating fractal-like intelligence hierarchies.

• Depth-1: Single agent for simple tasks
• Depth-2: Professor + 3-4 specialists for complex reasoning
• Depth-3+: Recursive hierarchies for research-grade problems

We welcome contributions! Areas of interest:

• Automated specialist discovery algorithms
• Cross-domain transfer learning
• Resource optimization for dynamic teams
• Integration with ML frameworks

See Contributing Guidelines for details.

@misc{tooliense2025crux,
  title  = {CRUX: Autonomous Mathematical Research through Hierarchical Multi-Agent Orchestration},
  author = {Tooliense Team},
  year   = {2025},
  note   = {IC-RL Implementation with Self-Evolve Mechanism},
  url    = {https://github.com/tooliense/crux}
}

MIT License. Please respect the terms of your model provider (OpenAI, DeepSeek, etc.).