arXiv Machine Learning By Carson Eisenach, Robert Joseph George, Vincent Quenneville-Belair, Kate Gwimm, Dean Foster

L3M: A Verifiable Harness and Runtime for Self-Extending and Self-Improving Agents

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L3M is a runtime built in Lean 4 that enables self‑extending and self‑improving agents to operate across humans, models, and code without requiring human attention in every loop. It stores all computation state in Git, allowing rich state trajectories that can be resumed, rewound, forked, compared, and merged. The system uses reversibility and kernel‑checked theorems to ensure safety, providing agents with sealed Lean programs as tools that can be reviewed and undone when necessary.

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