Gödel Machine Self-Optimizer

About

The Gödel Machine skill brings Jürgen Schmidhuber's vision of self-referential, universal problem solvers to the Claude Code environment. It enables the creation of systems capable of rewriting their own source code, including their learning algorithms, provided a formal proof can verify that the rewrite improves the system's utility. By integrating formal verification tools like Lean4 or Coq with LLM-based mutation and Darwinian evolutionary strategies, this skill provides a rigorous framework for developing autonomous agents and self-healing software that are both safe and asymptotically optimal.

Key Features

• Integration with theorem provers like Lean4 and Coq
• LLM-powered code mutation for generating candidate improvements
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• Darwinian evolutionary search for open-ended policy optimization
• Utility-based fitness evaluation for self-referential systems
• Formal proof-gated code rewriting to ensure modification safety

Use Cases

• Developing autonomous AI agents that safely evolve their own decision-making logic
• Creating self-healing software architectures that verify patches before application
• Optimizing complex algorithmic policies through mathematically proven code mutations