[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"fUxOy9L2we":3},"# Clawristotle: Semi-Autonomous Mathematical Research\n\n\u003Cp align=\"center\">\n  \u003Cimg src=\"artifacts/clawristotle.png\" alt=\"Clawristotle\" width=\"400\">\n\u003C/p>\n\n[![Lean Action CI](https://github.com/Vilin97/Clawristotle/actions/workflows/lean_action_ci.yml/badge.svg)](https://github.com/Vilin97/Clawristotle/actions/workflows/lean_action_ci.yml) [![Documentation](https://img.shields.io/badge/docs-blueprint-blue)](https://vilin97.github.io/Clawristotle/blueprint/) [![Dependency Graph](https://img.shields.io/badge/docs-dep_graph-blue)](https://vilin97.github.io/Clawristotle/blueprint/dep_graph_document.html) [![arXiv](https://img.shields.io/badge/arXiv-2603.15929-b31b1b)](https://arxiv.org/abs/2603.15929) [![Paper](https://img.shields.io/badge/HF-Paper-yellow)](https://huggingface.co/papers/2603.15929) [![Logs](https://img.shields.io/badge/HF-Agent_Logs-yellow)](https://huggingface.co/datasets/Vilin97/Clawristotle-Logs)\n\n> This README focuses on the autonomous agent system. For the detailed mathematical and technical report, see [TECHNICAL_REPORT.md](TECHNICAL_REPORT.md).\n\nA complete formalization of the Vlasov-Maxwell-Landau steady-state theorem on the 3-torus — achieved in 10 days by a centaur team of AI agents and a human mathematician.\n\n---\n\n## 🚀 The Result\n\n| Metric | Value |\n|--------|-------|\n| Status | ✅ Fully Verified (0 sorry's) |\n| Lean 4 Code | 10,445 lines |\n| Development Time | 10 days (Mar 1–10, 2026) |\n| Human Prompts | 229 |\n| Assistant Turns | 27,200+ |\n| Tokens Consumed | 2.8 Billion |\n| API Cost | ~$6,300 |\n\n> *\"The goal is not to end up with 0 sorry's! The goal is to make an honest formalization of the main theorem.\"* — [Project Manifesto](Aristotle/Landau/CLAUDE.md)\n\nThis project demonstrates a new paradigm in mathematical research: Semi-Autonomous Formalization. The human steers the high-level strategy and validates the definitions, while a suite of AI agents handles the implementation, proof search, and verification.\n\n## 🤖 The Team\n\nThis result was produced by a specialized multi-agent system:\n\n1. [Vasily Ilin](https://github.com/Vilin97) (Human): Architect & Reviewer. Designed the proof strategy, enforced hypothesis discipline, and audited critical definitions.\n2. [Claude Code](https://claude.com/claude-code) (Agent): Engineer & Prover. Wrote 99% of the Lean code, managed the repository, and executed the `/babysit` loop.\n3. [Gemini DeepThink](https://gemini.google.com) (Reasoning Model): Mathematician. Generated the initial natural-language proof and solved complex analytical bottlenecks.\n4. [Aristotle](https://aristotle.harmonic.fun/) (ATP): Lemma Specialist. Automatically proved 111 difficult lemmas and caught 28 false conjectures via counterexample search.\n\n## ⚡ The Engine: `/babysit`\n\nThe core innovation is the `/babysit` loop: an autonomous development cycle run by Claude Code.\n\n1. `/critique`: Adversarial review of the codebase (finding gaps, dead code, weak definitions).\n2. `/plan`: Prioritize work based on the critique.\n3. `/prove`: Attempt to close open `sorry`'s using Mathlib tactics.\n4. `/submit-aristotle`: Extract hard lemmas and send them to the Aristotle cloud prover.\n5. `/check-aristotle`: Integrate successful proofs and debug failed ones.\n6. `/simplify`: Refactor code and remove redundancy.\n\nThis loop ran continuously, often overnight, turning high-level directives into verified theorems.\n\n## 📊 Visualization\n\n### The Dependency Graph\n\n![Dependency graph](artifacts/dep_graph.png)\n*Every node represents a verified theorem. The graph flows from basic definitions to the final VML steady-state theorem.*\n\n### Velocity of Development\n\n![LOC History](artifacts/loc_history.png)\n*10,000 lines of verified code in 10 days. The sharp rise on Mar 7-8 represents the autonomous \"sprint\" to handle the Coulomb kernel singularity.*\n\n### Autonomous Activity\n\n![Session Activity](artifacts/session_activity.png)\n*Blue bars are AI actions; red bars are human prompts. The system ran effectively autonomously for long stretches (see Mar 9-10).*\n\n## 📚 The Mathematics\n\nTheorem ([CoulombConcreteTheorem42](Aristotle/Landau/main/CoulombConcreteTheorem42.lean#L69)):\nLet $f > 0$ be a smooth steady-state solution of the Vlasov-Maxwell-Landau system with Coulomb collisions on $\\mathbb{T}^3$. If $f$ has appropriate decay and regularity, then:\n\n1. $f$ is a global Maxwellian (thermodynamic equilibrium).\n2. The electric field $E$ vanishes everywhere.\n3. The magnetic field $B$ is constant.\n\nThis is a rigidity result fundamental to plasma physics, formalized here in full generality.\n\n## 🛠️ Tech Stack\n\n- Language: [Lean 4](https://leanprover.github.io/)\n- Library: [Mathlib](https://github.com/leanprover-community/mathlib4)\n- Agents: Claude Code, Gemini\n- Prover: Aristotle (Harmonic)\n\n## 📄 Resources\n\n- [Technical Report](https://huggingface.co/papers/2603.15929)\n- [Agent Logs Dataset](https://huggingface.co/datasets/Vilin97/Clawristotle-Logs)\n\n## 📄 License\n\nThis work is licensed under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/).\n",1780241990591]