🚀 CRUX

<p><em>The State-of-the-Art Intelligence</em></p> <img src="./assets/crux-github-banner.png" alt="Crux AI Banner" width="100%" style="border-radius: 15px; box-shadow: 0 8px 32px rgba(0,0,0,0.1);"> <p align="center"> <a href="https://tooliense.com"> 🌐 <strong>Who we are</strong> </a> • <a href="https://discord.gg/mP5YVp5gwK"> 💬 <strong>Join Discord</strong> </a> </p>

<h3>🧠 Breakthrough AI Research • 🎯 Mathematical Discovery • 🔬 Autonomous Problem Solving</h3> <p align="center"> <a href="2025_USAMO_p6.pdf"> <img src="https://img.shields.io/badge/Internal_Reasoning-9000%2B_Lines-FF4444?style=flat-square&logo=brain&logoColor=white" alt="Lines of Reasoning"/> </a> <a href="2025_USAMO_p6.pdf"> <img src="https://img.shields.io/badge/Problem_Level-USAMO_Grade-8A2BE2?style=flat-square&logo=graduation-cap&logoColor=white" alt="Problem Level"/> </a> <a href="TTRL-paper.pdf"> <img src="https://img.shields.io/badge/Research_Grade-Peer_Reviewed-00CED1?style=flat-square&logo=microscope&logoColor=white" alt="Research Quality"/> </a> <a href="TTRL-paper.pdf"> <img src="https://img.shields.io/badge/AI_Innovation-Autonomous_Discovery-FFD700?style=flat-square&logo=lightbulb&logoColor=white" alt="AI Innovation"/> </a> </p> <p align="center"> <a href="https://opensource.org/licenses/MIT"> <img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="License: MIT"/> </a> <a href="https://www.python.org/downloads/"> <img src="https://img.shields.io/badge/python-3.8+-blue.svg" alt="Python 3.8+"/> </a> <a href="https://openai.com/"> <img src="https://img.shields.io/badge/API-OpenAI-green.svg" alt="OpenAI"/> </a> <a href="https://deepseek.com/"> <img src="https://img.shields.io/badge/API-DeepSeek-purple.svg" alt="DeepSeek"/> </a> </p> </div> <br>

🎓 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.

🌟 Core Innovation: IC-RL (In-Context Reinforcement Learning)

Prompt ≙ Policy Parameters | Feedback ≙ Reward

We optimize the context itself, not the model weights.

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🏆 Key Achievements

🎯 2025 USAMO Problem 6 Complete Solution

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.

🔬 Independent TTRL Hypothesis Verification

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

🏗️ Enhanced Multi-Layer Agent Architecture

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.

Core Capabilities

| Feature | Description | | ----------------------------- | ----------------------------------------------------- | | 🧮 Mathematical Reasoning | Deep mathematical understanding with proof generation | | 🔍 Problem Analysis | Systematic breakdown of complex mathematical problems | | 📊 Theoretical Framework | Independent development of mathematical theories | | 🎯 USAMO-Level Solutions | Solving competition-grade mathematical problems | | 🔬 Research Methodology | Autonomous mathematical research and discovery |

Key Research Areas

Mathematics & Problem Solving

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

Theoretical AI Research

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

Research Methodology

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

Technical Specifications

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

Research Impact

Contributing to Research

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

Research Timeline

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

About Tooliense

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.

📁 Project Structure

🧠 Self-Evolve Core

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

🌐 Crux Agent Web Application

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

🚀 Quick Start

Option 1: Run Core Self-Evolve Engine

# 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

Option 2: Run Full Web Application

# 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.

💡 Technical Innovation

IC-RL: A New Paradigm

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

Hierarchical Agent Architecture

🎓 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.

Proven Scaling Behavior

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

📈 Performance Insights

| Metric | Basic Self-Evolve | Enhanced Architecture | | ---------------------- | ----------------- | --------------------- | | Problem Complexity | Medium | Ultra-High | | Reasoning Depth | ~100 lines | 9,000+ lines | | Success Rate | Good | Exceptional | | Scaling Ability | Limited | Unlimited |

🤝 Contributing

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.

📚 Citation

@misc{tooliense2025crux,
  title  = {CRUX: Autonomous Mathematical Research through Hier

Crux

Install / Use

README