Sep 17, 2026 · quant-phJ/K move · Enter open · S save
Sirui Lu, Ruixuan Deng, Yanqiao Zhu, Zhengfeng Ji
Max‑Planck‑Institut für Quantenoptik, Hans‑Kopfermann‑Straße 1, D‑85748 Garching, Germany · Munich Center for Quantum Science and Technology (MCQST), Schellingstraße 4, D‑80799 Munich, Germany · Department of Computer Science and Technology, Tsinghua University · Department of Computer Science, University of California, Los Angeles, Los Angeles, California, USA
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.