Long-horizon autoformalization of a core theorem underlying MIP* = RE

2026-09-17

AI Summary

研究解决了长时间跨度的定理形式化问题，通过开发FormalFlow系统协调AI证明代理在人类监督下工作，成功完成了MIP* = RE核心定理的形式化验证。

Abstract

Landmark mathematical formalizations have taken specialist teams years to complete. We present FormalFlow, a system that coordinates AI proving agents under human supervision to address statement drift and proof composition in long-horizon formalization. Drawing on software engineering principles and practices, it uses a shared blueprint to guide nested planning, proving and review loops. Agents strengthen verification and review throughout formalization. We completed a machine-checked Lean 4 proof of the quantum soundness of the classical low individual-degree test, a core theorem underlying MIP* = RE. Developing the proof took 63 days; greater parallelism could further reduce this time. The final library contains 126,367 lines of Lean code, all generated by agents. The formalization corrects side conditions and intermediate errors while preserving the published final error bound under corrected assumptions. This work provides a verified foundation for quantum complexity and demonstrates a route to affordable verification of major research proofs by small teams.

Problem

• long-horizon formalization
• statement drift
• proof composition

Innovation

• FormalFlow
• long-horizon formalization
• AI proving agents
• quantum soundness
• MIP* = RE